Inequalties
for
martingales, singular integrals
and related topics, a bibliography
Rodrigo Bañuelos and Prabhu
Janakiraman
| [1] | P. Janakiraman. Limiting
weak-type behavior for the
riesz
transform and maximal operator when λ to infinity. Preprint. [ bib ] |
| [2] | P. Janakiraman. Limiting
weak-type behavior for singular
integral
and maximal operators. {Submitted}. [ bib ] |
| [3] | F. W. Gehring. "open problems''
in proceedings of the
romanian-finnish seminar on teichmuller spaces and quasiconformal
mappings (brasov, romania). Acad. Soc. Rep. Romania, Bucharest
(1969), 306. [ bib ] |
| [4] | O. Dragicevic and
A. Volberg. Bellman functions,
littlewood-paley estiamtes and asymptotics for the Ahlfors-Beurling
operator in Lp, preprint. [ bib ] |
| [5] | O. Dragicevic and
A. Volberg. Bellman functions and
dimensionelss estimates of Riesz transforms, preprint. [ bib ] |
| [6] | A. J. Lindeman
R. Bañuelos. The
martingale
structure of the Beurling-Ahlfors transform. unpublished paper. [ bib | html ] |
| [7] | A. N. Kolmogorov. Sur les
fonctions harmoniques
conjugees et les
series de fourier. Fund. Math., 7:24-29, 1925. [ bib ] |
| [8] | Marcel Riesz. Sur les fonctions
conjuguées. Math.
Z.,
27(1):218-244, 1928. [ bib | http ] |
| [9] | R. E. A. C. Paley. A
remarkable series of
orthogonal
functions i. Proc. London Math. Soc., 34:241-264, 1932. [ bib ] |
| [10] | A. P. Calderon and
A. Zygmund. On the existence of
certain
singular integrals. Acta Math., 88:85-139, 1952. [ bib | http ] |
| [11] | J. L. Doob. Stochastic
processes. John Wiley
& Sons
Inc., New York, 1953. [ bib | http ] |
| [12] | B. V. Boyarski\i. Homeomorphic
solutions of Beltrami
systems. Dokl.
Akad. Nauk SSSR (N.S.), 102:661-664, 1955. [ bib | http ] |
| [13] | A. P. Calderón and
A. Zygmund. On singular
integrals. Amer.
J. Math., 78:289-309, 1956. [ bib | http ] |
| [14] | E. M. Stein and Guido Weiss. An
extension of a theorem
of
Marcinkiewicz and some of its applications. J. Math. Mech.,
8:263-284, 1959. [ bib | http ] |
| [15] | Benjamin Muckenhoupt. On certain
singular integrals. Pacific
J.
Math., 10:239-261, 1960. [ bib | http ] |
| [16] | Lars Hörmander. Estimates for
translation invariant
operators in Lp
spaces. Acta Math., 104:93-140, 1960. [ bib | http ] |
| [17] | F. John and L. Nirenberg.
On functions of bounded
mean
oscillation. Comm. Pure Appl. Math., 14:415-426, 1961. [ bib | http ] |
| [18] | Olli Lehto. Remarks on the
integrability of the derivatives
of
quasiconformal mappings. Ann. Acad. Sci. Fenn. Ser. A I No.,
371:8, 1965. [ bib | http ] |
| [19] | F. W. Gehring and E. Reich.
Area distortion under
quasiconformal mappings. Ann. Acad. Sci. Fenn. Ser. A I No.,
388:15, 1966. [ bib | http ] |
| [20] | D. L. Burkholder. Martingale
transforms. Ann. Math.
Statist.,
37:1494-1504, 1966. [ bib | http ] |
| [21] | A. M. Olevski\i. Fourier series
and Lebesgue functions. Uspehi
Mat. Nauk, 22(3 (135)):237-239, 1967. [ bib | http ] |
| [22] | Hiroshi Kunita and Shinzo Watanabe.
On square integrable
martingales. Nagoya
Math. J., 30:209-245, 1967. [ bib | http ] |
| [23] | Richard F. Gundy. The martingale
version of a theorem of
Marcinkiewicz and Zygmund. Ann. Math. Statist, 38:725-734,
1967. [ bib | http ] |
| [24] | A. Zygmund. Trigonometric
series: Vols. I, II.
Second
edition, reprinted with corrections and some additions. Cambridge
University Press, London, 1968. [ bib | http ] |
| [25] | Richard F. Gundy. A
decomposition for L1-bounded
martingales. Ann. Math. Statist., 39:134-138, 1968. [ bib | http ] |
| [26] | Richard F. Gundy. On a class of
martingale series. In Orthogonal
Expansions and their Continuous Analogues (Proc. Conf., Edwardsville,
Ill., 1967), pages 99-102. Southern Illinois Univ. Press,
Carbondale, Ill., 1968. [ bib | http ] |
| [27] | Richard F. Gundy. On the class L logL,
martingales, and singular integrals. Studia Math.,
33:109-118, 1969. [ bib | http ] |
| [28] | Elias M. Stein. Singular
integrals and
differentiability
properties of functions. Princeton Mathematical Series, No. 30.
Princeton University Press, Princeton, N.J., 1970. [ bib | http ] |
| [29] | D. L. Burkholder and R. F.
Gundy. Extrapolation and
interpolation of quasi-linear operators on martingales. Acta Math.,
124:249-304, 1970. [ bib | http ] |
| [30] | Elias M. Stein and Guido Weiss. Introduction
to
Fourier
analysis on Euclidean spaces. Princeton University Press,
Princeton, N.J., 1971. [ bib | http ] |
| [31] | D. L. Burkholder, R. F.
Gundy, and M. L.
Silverstein. A
maximal function characterization of the class Hp. Trans.
Amer. Math. Soc., 157:137-153, 1971. [ bib | http ] |
| [32] | S. K. Pichorides. On the best
values of the constants in
the
theorems of M. Riesz, Zygmund and Kolmogorov. Studia Math.,
44:165-179. (errata insert), 1972. [ bib | http ] |
| [33] | D. L. Burkholder, B. J.
Davis, and R. F.
Gundy. Integral
inequalities for convex functions of operators on martingales. In Proceedings
of the Sixth Berkeley Symposium on Mathematical Statistics and
Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II:
Probability theory, pages 223-240, Berkeley, Calif., 1972. Univ.
California Press. [ bib | http ] |
| [34] | O. Lehto and K. I.
Virtanen. Quasiconformal
mappings in
the plane. Springer-Verlag, New York, 1973. [ bib | http ] |
| [35] | F. W. Gehring. The Lp-integrability
of the
partial derivatives of a quasiconformal mapping. Acta Math.,
130:265-277, 1973. [ bib | http ] |
| [36] | Burgess Davis. On the distributions
of conjugate functions of
nonnegative measures. Duke Math. J., 40:695-700, 1973. [ bib | http ] |
| [37] | D. L. Burkholder and R. F.
Gundy. Boundary
behaviour of
harmonic functions in a half-space and Brownian motion. Ann. Inst.
Fourier (Grenoble), 23(4):195-212, 1973. [ bib | http ] |
| [38] | D. L. Burkholder. Distribution
function inequalities for
martingales. Ann. Probability, 1:19-42, 1973. [ bib | http ] |
| [39] | H. M. Reimann. Functions of
bounded mean oscillation and
quasiconformal mappings. Comment. Math. Helv., 49:260-276,
1974. [ bib | http ] |
| [40] | Burgess Davis. On the weak type (1,1)
inequality for
conjugate
functions. Proc. Amer. Math. Soc., 44:307-311, 1974. [ bib | http ] |
| [41] | Bogdan Bojarski and T. Iwaniec.
Quasiconformal mappings
and
non-linear elliptic equations in two variables. I, II. Bull. Acad.
Polon. Sci. Sér. Sci. Math. Astronom. Phys., 22:473-478;
ibid. 22 (1974), 479-484, 1974. [ bib | http ] |
| [42] | B. Maurey. Système de
Haar. In Séminaire
Maurey-Schwartz 1974-1975: Espaces Lp, applications
radonifiantes et géométrie des espaces
Banach, Exp.
Nos. I et II pages 26 pp. (erratum, p. 1). Centre Math.,
École Polytech., Paris, 1975. [ bib | http ] |
| [43] | Charles Fefferman. Recent progress in
classical Fourier
analysis. In Proceedings
of the International Congress of Mathematicians (Vancouver, B.C.,
1974), Vol. 1, pages 95-118. Canad. Math. Congress, Montreal,
Que., 1975. [ bib | http ] |
| [44] | Olli Lehto. Quasiconformal mappings
and singular integrals.
In Symposia
Mathematica, Vol. XVIII (Convegno sulle Transformazioni Quasiconformi e
Questioni Connesse, INDAM, Rome, 1974), pages 429-453. Academic
Press, London, 1976. [ bib | http ] |
| [45] | R. F. Gundy and N. Th.
Varopoulos. A martingale
that occurs
in harmonic analysis. Ark. Mat., 14(2):179-187, 1976. [ bib | http ] |
| [46] | Burgess Davis. On the Lp
norms of
stochastic
integrals and other martingales. Duke Math. J.,
43(4):697-704, 1976. [ bib | http ] |
| [47] | D. L. Burkholder. Harmonic
analysis and probability. In Studies
in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974),
pages 136-149. MAA Stud. Math., Vol. 13. Math. Assoc. Amer.,
Washington, D.C., 1976. [ bib | http ] |
| [48] | Bogdan Bojarski. Quasiconformal
mappings and general
structural
properties of systems of non linear equations elliptic in the sense of
Lavrent ev. In Symposia Mathematica, Vol. XVIII (Convegno sulle
Transformazioni Quasiconformi e Questioni Connesse, INDAM, Rome, 1974),
pages 485-499. Academic Press, London, 1976. [ bib | http ] |
| [49] | D. L. Burkholder. Exit times of
Brownian motion,
harmonic
majorization, and Hardy spaces. Advances in Math.,
26(2):182-205, 1977. [ bib | http ] |
| [50] | N. Th. Varopoulos. A remark on
functions of bounded mean
oscillation and bounded harmonic functions. Addendum to: ``BMO
functions and the -equation'' (Pacific J. Math. 71 (1977), no.
1, 221-273). Pacific J. Math., 74(1):257-259, 1978. [ bib | http ] |
| [51] | Albert Baernstein, II. Some sharp
inequalities for conjugate
functions. Indiana Univ. Math. J., 27(5):833-852, 1978. [ bib | http ] |
| [52] | N. Th. Varopoulos. B.M.O.
functions in complex analysis.
In Harmonic
analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll.,
Williamstown, Mass., 1978), Part 2, Proc. Sympos. Pure Math.,
XXXV, Part, pages 43-61. Amer. Math. Soc., Providence, R.I., 1979. [ bib | http ] |
| [53] | Richard F. Gundy and Nicolas
Th. and Varopoulos.
Les
transformations de Riesz et les intégrales stochastiques. C.
R. Acad. Sci. Paris Sér. A-B, 289(1):A13-A16, 1979. [ bib | http ] |
| [54] | Burgess Davis. Brownian motion and
analytic functions. Ann.
Probab.,
7(6):913-932, 1979. [ bib | http ] |
| [55] | Burgess Davis. Applications of the
conformal invariance of
Brownian
motion. In Harmonic analysis in Euclidean spaces (Proc. Sympos.
Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 2,
Proc. Sympos. Pure Math., XXXV, Part, pages 303-310. Amer. Math. Soc.,
Providence, R.I., 1979. [ bib | http ] |
| [56] | Nicolas Th. and Varopoulos.
Aspects of probabilistic
Littlewood-Paley theory. J. Funct. Anal., 38(1):25-60, 1980. [ bib | http ] |
| [57] | Peter W. and Jones. Extension
theorems for BMO. Indiana
Univ.
Math. J., 29(1):41-66, 1980. [ bib | http ] |
| [58] | R. F. Gundy. Maximal function
characterization of Hp
for the bidisc. In Harmonic analysis, Iraklion 1978 (Proc. Conf.,
Univ. Crete, Iraklion, 1978), volume 781 of Lecture Notes in
Math., pages 51-58. Springer, Berlin, 1980. [ bib | http ] |
| [59] | R. F. Gundy.
Inégalités pour martingales
à un
et deux indices: l'espace Hp. In Eighth Saint
Flour Probability Summer School-1978 (Saint Flour, 1978), volume
774 of Lecture Notes in Math., pages 251-334. Springer,
Berlin, 1980. [ bib | http ] |
| [60] | Burgess Davis. Hardy spaces and
rearrangements. Trans.
Amer. Math.
Soc., 261(1):211-233, 1980. [ bib | http ] |
| [61] | Nicolas Th. Varopoulos. A
theorem on weak type estimates
for Riesz
transforms and martingale transforms. Ann. Inst. Fourier (Grenoble),
31(1):viii, 257-264, 1981. [ bib | http ] |
| [62] | Nicholas Th. Varopoulos.
Probabilistic approach to some
problems
in complex analysis. Bull. Sci. Math. (2), 105(2):181-224,
1981. [ bib | http ] |
| [63] | Elias M. Stein, Mitchell H.
Taibleson, and Guido
Weiss. Weak
type estimates for maximal operators on certain Hp
classes. Rend. Circ. Mat. Palermo (2), (suppl. 1):81-97, 1981. [ bib | http ] |
| [64] | D. L. Burkholder. A geometrical
characterization of
Banach spaces
in which martingale difference sequences are unconditional. Ann.
Probab., 9(6):997-1011, 1981. [ bib | http ] |
| [65] | T. Iwaniec. Extremal
inequalities in Sobolev spaces and
quasiconformal mappings. Z. Anal. Anwendungen, 1(6):1-16,
1982. [ bib | http ] |
| [66] | Richard F. Gundy and
Martin L. Silverstein. On a
probabilistic interpretation for the Riesz transforms. In Functional
analysis in Markov processes (Katata/Kyoto, 1981), volume 923 of Lecture
Notes in Math., pages 199-203. Springer, Berlin, 1982. [ bib | http ] |
| [67] | Claude Dellacherie and
Paul-André Meyer. Probabilities
and
potential. B, volume 72 of North-Holland Mathematics
Studies. North-Holland Publishing Co., Amsterdam, 1982. [ bib | http ] |
| [68] | D. L. Burkholder. A nonlinear
partial differential
equation and
the unconditional constant of the Haar system in Lp.
Bull. Amer. Math. Soc. (N.S.), 7(3):591-595, 1982. [ bib | http ] |
| [69] | E. M. Stein and J.-O.
Strömberg. Behavior of
maximal
functions in Rn for large n. Ark. Mat.,
21(2):259-269, 1983. [ bib | http ] |
| [70] | E. M. Stein. Some results in
harmonic analysis in Rn,
for n-> . Bull. Amer. Math. Soc. (N.S.),
9(1):71-73, 1983. [ bib | http ] |
| [71] | D. L. Burkholder. A geometric
condition that implies the
existence
of certain singular integrals of Banach-space-valued functions. In Conference
on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago,
Ill., 1981), Wadsworth Math. Ser., pages 270-286. Wadsworth,
Belmont, CA, 1983. [ bib | http ] |
| [72] | J. Bourgain. Some remarks on
Banach spaces in which
martingale
difference sequences are unconditional. Ark. Mat.,
21(2):163-168, 1983. [ bib | http ] |
| [73] | Albert Baernstein, II and
Juan J. Manfredi. Topics in
quasiconformal mapping. In Topics in modern harmonic analysis,
Vol. I, II (Turin/Milan, 1982), pages 819-862. Ist. Naz. Alta Mat.
Francesco Severi, Rome, 1983. [ bib | http ] |
| [74] | I.E. Verbitsky. An estimate of the
norm of a function in
hardy space in
terms of the norm of its real and imaginary parts. Amer. Math.
Soc. Transl, 124:11-15, 1984. [ bib ] |
| [75] | Terry R. McConnell. On Fourier
multiplier
transformations of
Banach-valued functions. Trans. Amer. Math. Soc.,
285(2):739-757, 1984. [ bib | http ] |
| [76] | T. Figiel, T. Iwaniec, and
A. Pelczynski.
Computing
norms and critical exponents of some operators in L p-spaces.
Studia Math., 79(3):227-274, 1984. [ bib | http ] |
| [77] | Richard Durrett. Brownian motion
and martingales in
analysis.
Wadsworth Mathematics Series. Wadsworth International Group, Belmont,
CA, 1984. [ bib | http ] |
| [78] | D. L. Burkholder. Boundary value
problems and sharp
inequalities
for martingale transforms. Ann. Probab., 12(3):647-702, 1984. [ bib | http ] |
| [79] | Boguslaw Tomaszewski. Some sharp
weak-type inequalities for
holomorphic
functions on the unit ball of C n. Proc. Amer.
Math. Soc., 95(2):271-274, 1985. [ bib | http ] |
| [80] | A. Pelczynski. Norms of
classical operators in function
spaces. Astérisque,
(131):137-162, 1985. [ bib | http ] |
| [81] | R. F. Gundy and M. L.
Silverstein. The density of
the area
integral in R n+1 +. Ann. Inst. Fourier
(Grenoble), 35(1):215-229, 1985. [ bib | http ] |
| [82] | José García-Cuerva and
José L.
Rubio de
Francia. Weighted norm inequalities and related topics,
volume 116 of North-Holland Mathematics Studies.
North-Holland Publishing Co., Amsterdam, 1985. [ bib | http ] |
| [83] | Javier Duoandikoetxea and
José L. Rubio de
Francia.
Estimations indépendantes de la dimension pour les
transformées de Riesz. C. R. Acad. Sci. Paris Sér. I
Math., 300(7):193-196, 1985. [ bib | http ] |
| [84] | D. L. Burkholder. An elementary
proof of an inequality
of R. E. A.
C. Paley. Bull. London Math. Soc., 17(5):474-478, 1985. [ bib | http ] |
| [85] | T. Iwaniec. The best constant in
a BMO-inequality for
the
Beurling-Ahlfors transform. Michigan Math. J., 33(3):387-394,
1986. [ bib | http ] |
| [86] | Richard F. Gundy. Sur les
transformations de Riesz pour
le
semi-groupe d'Ornstein-Uhlenbeck. C. R. Acad. Sci. Paris
Sér. I Math., 303(19):967-970, 1986. [ bib | http ] |
| [87] | Donald L. Burkholder.
Martingales and Fourier analysis
in Banach
spaces. In Probability and analysis (Varenna, 1985), volume
1206 of Lecture Notes in Math., pages 61-108. Springer,
Berlin, 1986. [ bib | http ] |
| [88] | J. Bourgain and
W. J. and Davis. Martingale
transforms
and complex uniform convexity. Trans. Amer. Math. Soc.,
294(2):501-515, 1986. [ bib | http ] |
| [89] | Jean Bourgain. Vector-valued singular
integrals and the H
1-BMO duality. In Probability theory and harmonic analysis
(Cleveland, Ohio, 1983), volume 98 of Monogr. Textbooks
Pure Appl. Math., pages 1-19. Dekker, New York, 1986. [ bib | http ] |
| [90] | Rodrigo Bañuelos. Martingale
transforms and related
singular
integrals. Trans. Amer. Math. Soc., 293(2):547-563, 1986. [ bib | http ] |
| [91] | E. M. Stein. Problems in
harmonic analysis related to
curvature
and oscillatory integrals. In Proceedings of the International
Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986),
pages 196-221, Providence, RI, 1987. Amer. Math. Soc. [ bib | http ] |
| [92] | Tadeusz Iwaniec. Hilbert transform in
the complex plane and
area
inequalities for certain quadratic differentials. Michigan Math. J.,
34(3):407-434, 1987. [ bib | http ] |
| [93] | F. W. Gehring. Topics in
quasiconformal mappings. In Proceedings
of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley,
Calif., 1986), pages 62-80, Providence, RI, 1987. Amer. Math. Soc. [ bib | http ] |
| [94] | D. L. Burkholder. A sharp and
strict L p-inequality
for stochastic integrals. Ann. Probab., 15(1):268-273, 1987. [ bib | http ] |
| [95] | Rodrigo Bañuelos. A note on
martingale transforms and A p-weights. Studia
Math., 85(2):125-135, 1987. [ bib | http ] |
| [96] | Gilles Pisier. Riesz transforms: a
simpler analytic proof of
P.-A.
Meyer's inequality. In Séminaire de Probabilités,
XXII, volume 1321 of Lecture Notes in Math., pages
485-501. Springer, Berlin, 1988. [ bib | http ] |
| [97] | Donald L. Burkholder. Sharp
inequalities for martingales
and
stochastic integrals. Astérisque, (157-158):75-94,
1988. [ bib | http ] |
| [98] | Rodrigo Bañuelos and
Andrew G. Bennett.
Paraproducts and
commutators of martingale transforms. Proc. Amer. Math. Soc.,
103(4):1226-1234, 1988. [ bib | http ] |
| [99] | Rodrigo Bañuelos. A sharp
good-λ inequality with an
application
to Riesz transforms. Michigan Math. J., 35(1):117-125, 1988. [ bib | http ] |
| [100] | R. F. Gundy. Some martingale
inequalities with
applications to
harmonic analysis. J. Funct. Anal., 87(1):212-230, 1989. [ bib | http ] |
| [101] | Richard F. Gundy. Some
topics in probability and
analysis,
volume 70 of CBMS Regional Conference Series in Mathematics.
Published for the Conference Board of the Mathematical Sciences,
Washington, DC, 1989. [ bib | http ] |
| [102] | S. K. Donaldson and D. P.
Sullivan. Quasiconformal
4-manifolds. Acta Math., 163(3-4):181-252, 1989. [ bib | http ] |
| [103] | Bernard Dacorogna. Direct
methods in the calculus of
variations,
volume 78 of Applied Mathematical Sciences.
Springer-Verlag, Berlin, 1989. [ bib | http ] |
| [104] | Donald L. Burkholder.
Differential subordination of
harmonic
functions and martingales. In Harmonic analysis and partial
differential equations (El Escorial, 1987), volume 1384 of Lecture
Notes in Math., pages 1-23. Springer, Berlin, 1989. [ bib | http ] |
| [105] | Donald L. Burkholder. On the
number of escapes of a
martingale and
its geometrical significance. In Almost everywhere convergence
(Columbus, OH, 1988), pages 159-178. Academic Press, Boston, MA,
1989. [ bib | http ] |
| [106] | Vladimír Sverák.
Examples of rank-one convex
functions. Proc.
Roy. Soc. Edinburgh Sect. A, 114(3-4):237-242, 1990. [ bib | http ] |
| [107] | B. Dacorogna, J. Douchet,
W. Gangbo, and
J. Rappaz.
Some examples of rank one convex functions in dimension two. Proc.
Roy. Soc. Edinburgh Sect. A, 114(1-2):135-150, 1990. [ bib | http ] |
| [108] | Gang and Wang. Sharp
square-function inequalities for
conditionally symmetric martingales. Trans. Amer. Math. Soc.,
328(1):393-419, 1991. [ bib | http ] |
| [109] | Gang and Wang. Sharp maximal
inequalities for
conditionally
symmetric martingales and Brownian motion. Proc. Amer. Math. Soc.,
112(2):579-586, 1991. [ bib | http ] |
| [110] | Gang and Wang. Sharp
inequalities for the conditional
square
function of a martingale. Ann. Probab., 19(4):1679-1688, 1991. [ bib | http ] |
| [111] | Donald L. Burkholder.
Explorations in martingale theory
and its
applications. In École d'Été de
Probabilités de Saint-Flour XIX-1989, volume 1464 of Lecture
Notes in Math., pages 1-66. Springer, Berlin, 1991. [ bib | http ] |
| [112] | Vladimír Sverák. New
examples of quasiconvex
functions. Arch.
Rational Mech. Anal., 119(4):293-300, 1992. [ bib | http ] |
| [113] | Vladimír Sverák.
Rank-one convexity does not
imply
quasiconvexity. Proc. Roy. Soc. Edinburgh Sect. A,
120(1-2):185-189, 1992. [ bib | http ] |
| [114] | Tadeusz Iwaniec. L p-theory
of
quasiregular
mappings. In Quasiconformal space mappings, volume 1508 of Lecture
Notes in Math., pages 39-64. Springer, Berlin, 1992. [ bib | http ] |
| [115] | Sheldon Axler, Paul Bourdon, and Wade
Ramey. Harmonic
function
theory, volume 137 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1992. [ bib | http ] |
| [116] | Elias M. Stein. Harmonic
analysis: real-variable
methods,
orthogonality, and oscillatory integrals, volume 43 of Princeton
Mathematical Series. Princeton University Press, Princeton, NJ,
1993. [ bib | http ] |
| [117] | Tadeusz Iwaniec and Gaven Martin.
Quasiregular mappings in
even
dimensions. Acta Math., 170(1):29-81, 1993. [ bib | http ] |
| [118] | Tadeusz Iwaniec and Adam Lutoborski.
Integral estimates for
null
Lagrangians. Arch. Rational Mech. Anal., 125(1):25-79, 1993. [ bib | http ] |
| [119] | E. B. Fabes. Gaussian upper
bounds on fundamental
solutions of
parabolic equations; the method of Nash. In Dirichlet forms
(Varenna, 1992), volume 1563 of Lecture Notes in Math.,
pages 1-20. Springer, Berlin, 1993. [ bib | http ] |
| [120] | Stephen M. Buckley. Estimates
for operator norms on
weighted
spaces and reverse Jensen inequalities. Trans. Amer. Math. Soc.,
340(1):253-272, 1993. [ bib | http ] |
| [121] | K. Astala, J. L.
Fernández, , and
S. and Rohde.
Quasilines and the Hayman-Wu theorem. Indiana Univ. Math. J.,
42(4):1077-1100, 1993. [ bib | http ] |
| [122] | Kari Astala. Distortion of area and
dimension under
quasiconformal
mappings in the plane. Proc. Nat. Acad. Sci. U.S.A.,
90(24):11958-11959, 1993. [ bib | http ] |
| [123] | N.Ya. Krupnik and I.E. Vertisky. The
norm of the riesz
projection. In Linear
and Complex Analysis Problems Book 3, Part I. Lecture Notes in
Mathemtics 1543. Edited by V.P. Havin and N.K. Nokolski. Springer,
1994. [ bib ] |
| [124] | T. Iwaniec, L. Migliaccio,
L. Nania, and
C. Sbordone. Integrability and removability results for
quasiregular mappings in high dimensions. Math. Scand.,
75(2):263-279, 1994. [ bib | http ] |
| [125] | Cristian E. Gutiérrez. On
the Riesz transforms
for Gaussian
measures. J. Funct. Anal., 120(1):107-134, 1994. [ bib | http ] |
| [126] | Eugene B. Fabes,
Cristian E. Gutiérrez, and
Roberto
Scotto. Weak-type estimates for the Riesz transforms associated with
the Gaussian measure. Rev. Mat. Iberoamericana,
10(2):229-281, 1994. [ bib | http ] |
| [127] | Bernard Dacorogna. Some recent
results on polyconvex,
quasiconvex and
rank one convex functions. In Calculus of variations,
homogenization and continuum mechanics (Marseille, 1993),
volume 18 of Ser. Adv. Math. Appl. Sci., pages 169-176.
World Sci. Publishing, River Edge, NJ, 1994. [ bib | http ] |
| [128] | Donald L. Burkholder. Strong
differential subordination
and
stochastic integration. Ann. Probab., 22(2):995-1025, 1994. [ bib | http ] |
| [129] | K. Astala and
M. Zinsmeister. Holomorphic families
of
quasi-Fuchsian groups. Ergodic Theory Dynam. Systems,
14(2):207-212, 1994. [ bib | http ] |
| [130] | Kari Astala. Area distortion of
quasiconformal mappings. Acta
Math.,
173(1):37-60, 1994. [ bib | http ] |
| [131] | Gang and Wang. Differential
subordination and strong
differential
subordination for continuous-time martingales and related sharp
inequalities. Ann. Probab., 23(2):522-551, 1995. [ bib | http ] |
| [132] | Richard Rochberg. Size estimates for
eigenvalues of singular
integral
operators and Schrödinger operators and for derivatives of
quasiconformal mappings. Amer. J. Math., 117(3):711-771, 1995. [ bib | http ] |
| [133] | A. Erëmenko and D. H.
Hamilton. On the area
distortion
by quasiconformal mappings. Proc. Amer. Math. Soc.,
123(9):2793-2797, 1995. [ bib | http ] |
| [134] | Richard F. Bass. Probabilistic
techniques in
analysis.
Probability and its Applications (New York). Springer-Verlag, New York,
1995. [ bib | http ] |
| [135] | Rodrigo Bañuelos and
Gang and Wang. Sharp
inequalities for
martingales with applications to the Beurling-Ahlfors and Riesz
transforms. Duke Math. J., 80(3):575-600, 1995. [ bib | http ] |
| [136] | K. Astala and
M. Zinsmeister. Abelian coverings,
Poincaré exponent of convergence and holomorphic deformations. Ann.
Acad. Sci. Fenn. Ser. A I Math., 20(1):81-86, 1995. [ bib | http ] |
| [137] | Kari Astala and Michel Zinsmeister.
Rectifiability in
Teichmüller
theory. In Topics in complex analysis (Warsaw, 1992),
volume 31 of Banach Center Publ., pages 45-52. Polish
Acad. Sci., Warsaw, 1995. [ bib | http ] |
| [138] | Kari Astala. The many faces of
mathematics. Arkhimedes,
47(4):308-319, 1995. [ bib | http ] |
| [139] | V. Nesi. Quasiconformal mappings
as a tool to study
certain
two-dimensional G-closure problems. Arch. Rational Mech.
Anal., 134(1):17-51, 1996. [ bib | http ] |
| [140] | Tadeusz Iwaniec and Gaven Martin.
Riesz transforms and
related singular
integrals. J. Reine Angew. Math., 473:25-57, 1996. [ bib | http ] |
| [141] | Cristian E. Gutiérrez,
Carlos Segovia, and
José
Luis and Torrea. On higher Riesz transforms for Gaussian measures.
J. Fourier Anal. Appl., 2(6):583-596, 1996. [ bib | http ] |
| [142] | R. Ba nuelos and G. Wang.
Sharp inequalities for
martingales
under orthogonality and differential subordination. 40:687-691, 1996. [ bib ] |
| [143] | Kari Astala, Lassi
Päivärinta, and Eero Saksman.
The finite
Hilbert transform in weighted spaces. Proc. Roy. Soc. Edinburgh
Sect. A, 126(6):1157-1167, 1996. [ bib | http ] |
| [144] | Loukas Grafakos and Stephen
Montgomery-Smith. Best constants
for
uncentred maximal functions. Bull. London Math. Soc.,
29(1):60-64, 1997. [ bib | http ] |
| [145] | Loukas Grafakos. Best bounds for the
Hilbert transform on L p(R
1). Math. Res. Lett., 4(4):469-471, 1997. [ bib | http ] |
| [146] | Loukas Grafakos. H 1
boundedness of determinants of
vector
fields. Proc. Amer. Math. Soc., 125(11):3279-3288, 1997. [ bib | http ] |
| [147] | Donald L. Burkholder. Sharp norm
comparison of
martingale maximal
functions and stochastic integrals. In Proceedings of the Norbert
Wiener Centenary Congress, 1994 (East Lansing, MI, 1994),
volume 52 of Proc. Sympos. Appl. Math., pages 343-358,
Providence, RI, 1997. Amer. Math. Soc. [ bib | http ] |
| [148] | Rodrigo Bañuelos and Arthur
Lindeman, II. A martingale
study of
the Beurling-Ahlfors transform in R n. J.
Funct. Anal., 145(1):224-265, 1997. [ bib | http ] |
| [149] | Nicola Arcozzi and Xinwei Li. Riesz
transforms on spheres. Math.
Res. Lett., 4(2-3):401-412, 1997. [ bib | http ] |
| [150] | T. Iwaniec and C. Sbordone.
Riesz transforms and
elliptic
PDEs with VMO coefficients. J. Anal. Math., 74:183-212, 1998. [ bib | http ] |
| [151] | Loukas Grafakos and Atanas Stefanov. L
p
bounds for
singular integrals and maximal singular integrals with rough kernels. Indiana
Univ. Math. J., 47(2):455-469, 1998. [ bib | http ] |
| [152] | L. Grafakos and
J. Kinnunen. Sharp inequalities for
maximal
functions associated with general measures. Proc. Roy. Soc.
Edinburgh Sect. A, 128(4):717-723, 1998. [ bib | http ] |
| [153] | Liliana Forzani and Roberto Scotto.
The higher order Riesz
transform
for Gaussian measure need not be of weak type (1,1). Studia Math.,
131(3):205-214, 1998. [ bib | http ] |
| [154] | Changsun Choi. A weak-type inequality
for differentially
subordinate
harmonic functions. Trans. Amer. Math. Soc.,
350(7):2687-2696, 1998. [ bib | http ] |
| [155] | Kari Astala and Markku Miettinen. On
quasiconformal mappings
and
2-dimensional G-closure problems. Arch. Rational Mech.
Anal., 143(3):207-240, 1998. [ bib | http ] |
| [156] | Kari Astala. Analytic aspects of
quasiconformality. Doc.
Math.,
(Extra Vol. II):617-626 (electronic), 1998. [ bib | http ] |
| [157] | Kari Astala. Recent connections and
applications of planar
quasiconformal mappings. In European Congress of Mathematics, Vol.
I (Budapest, 1996), volume 168 of Progr. Math., pages
36-51. Birkhäuser, Basel, 1998. [ bib | http ] |
| [158] | Kari Astala. Planar quasiconformal
mappings; deformations and
interactions. In Quasiconformal mappings and analysis (Ann Arbor,
MI, 1995), pages 33-54. Springer, New York, 1998. [ bib | http ] |
| [159] | Nicola Arcozzi and Luigi Fontana. A
characterization of the
Hilbert
transform. Proc. Amer. Math. Soc., 126(6):1747-1749, 1998. [ bib | http ] |
| [160] | Nicola Arcozzi. Riesz transforms on
compact Lie groups,
spheres and
Gauss space. Ark. Mat., 36(2):201-231, 1998. [ bib | http ] |
| [161] | F. Nazarov, , S. Treil, and
A. Volberg. The
Bellman
functions and two-weight inequalities for Haar multipliers. J.
Amer. Math. Soc., 12(4):909-928, 1999. [ bib | http ] |
| [162] | Loukas Grafakos, Stephen
Montgomery-Smith, and Olexei
Motrunich. A
sharp estimate for the Hardy-Littlewood maximal function. Studia
Math., 134(1):57-67, 1999. [ bib | http ] |
| [163] | Eugene Fabes, Irina Mitrea, and
Marius Mitrea. On the
boundedness of
singular integrals. Pacific J. Math., 189(1):21-29, 1999. [ bib | http ] |
| [164] | Donald L. Burkholder. Some
extremal problems in
martingale theory
and harmonic analysis. In Harmonic analysis and partial
differential equations (Chicago, IL, 1996), Chicago Lectures in
Math., pages 99-115. Univ. Chicago Press, Chicago, IL, 1999. [ bib | http ] |
| [165] | Rodrigo Bañuelos and Charles
N. and Moore. Probabilistic
behavior of harmonic functions, volume 175 of Progress in
Mathematics. Birkhäuser Verlag, Basel, 1999. [ bib | http ] |
| [166] | Albert Baernstein, II and
Stephen J. Montgomery-Smith.
Some
conjectures about integral means of f and f. In Complex
analysis and differential equations (Uppsala, 1997),
volume 64 of Acta Univ. Upsaliensis Skr. Uppsala Univ. C
Organ. Hist., pages 92-109. Uppsala Univ., Uppsala, 1999. [ bib | http ] |
| [167] | Nicola Arcozzi. L p
estimates for systems
of
conjugate harmonic functions. In Complex analysis and differential
equations (Uppsala, 1997), volume 64 of Acta Univ.
Upsaliensis Skr. Uppsala Univ. C Organ. Hist., pages 61-68.
Uppsala Univ., Uppsala, 1999. [ bib | http ] |
| [168] | Teresa Martínez and
José L. and Torrea.
Operator-valued martingale transforms. Tohoku Math. J. (2),
52(3):449-474, 2000. [ bib | http ] |
| [169] | Juha Kinnunen and Olli Martio.
Maximal operator and
superharmonicity.
In Function spaces, differential operators and nonlinear analysis
(Pudasjärvi, 1999), pages 157-169. Acad. Sci. Czech Repub.,
Prague, 2000. [ bib | http ] |
| [170] | Liliana Forzani, Roberto Scotto, and
Wilfredo Urbina. Riesz
and Bessel
potentials, the g k functions and an area function
for the Gaussian measure γ. Rev. Un. Mat. Argentina,
42(1):17-37 (2001), 2000. [ bib | http ] |
| [171] | M. Essén. On sharp
constants in the weak-type
(p,p)-inequalities, 2<p< . Report No. 43 Instit
Mittag-Leffler, 2000. [ bib ] |
| [172] | Rodrigo Bañuelos and
Gang and Wang. Davis's
inequality for
orthogonal martingales under differential subordination. Michigan
Math. J., 47(1):109-124, 2000. [ bib | http ] |
| [173] | Kari Astala, Tadeusz Iwaniec, Pekka
Koskela, and Gaven
Martin. Mappings
of BMO-bounded distortion. Math. Ann., 317(4):703-726, 2000. [ bib | http ] |
| [174] | Kari Astala, Zoltan Balogh, , and
Hans Martin Reimann.
Lempert
mappings and holomorphic motions in C n. Astérisque,
(261):xi, 1-12, 2000. [ bib | http ] |
| [175] | Tadeusz Iwaniec and Gaven Martin.
What's new for the Beltrami
equation?
In Geometric analysis and applications (Canberra, 2000),
volume 39 of Proc. Centre Math. Appl. Austral. Nat. Univ.,
pages 132-148. Austral. Nat. Univ., Canberra, 2001. [ bib | http ] |
| [176] | Tadeusz Iwaniec and Gaven Martin. Geometric
function
theory and
non-linear analysis. Oxford Mathematical Monographs. The Clarendon
Press Oxford University Press, New York, 2001. [ bib | http ] |
| [177] | Loukas Grafakos and Nigel Kalton.
Some remarks on multilinear
maps and
interpolation. Math. Ann., 319(1):151-180, 2001. [ bib | http ] |
| [178] | Liliana Forzani, Roberto Scotto, and
Wilfredo Urbina. A
simple proof of
the L p continuity of the higher order Riesz
transforms with respect to the Gaussian measure γ d. In Séminaire
de Probabilités, XXXV, volume 1755 of Lecture Notes
in Math., pages 162-166. Springer, Berlin, 2001. [ bib | http ] |
| [179] | Javier Duoandikoetxea. Fourier
analysis,
volume 29 of Graduate
Studies in Mathematics. American Mathematical Society, Providence,
RI, 2001. [ bib | http ] |
| [180] | Donald L. Burkholder.
Martingales and singular integrals
in Banach
spaces. In Handbook of the geometry of Banach spaces, Vol. I,
pages 233-269. North-Holland, Amsterdam, 2001. [ bib | http ] |
| [181] | K. Astala and G. J. Martin.
Holomorphic motions. In Papers
on analysis, volume 83 of Rep. Univ. Jyväskylä
Dep. Math. Stat., pages 27-40. Univ. Jyväskylä,
Jyväskylä, 2001. [ bib | http ] |
| [182] | Kari Astala, Tadeusz Iwaniec, and
Eero Saksman. Beltrami
operators in
the plane. Duke Math. J., 107(1):27-56, 2001. [ bib | http ] |
| [183] | S. Petermichl and J. and
Wittwer. A sharp estimate
for the
weighted Hilbert transform via Bellman functions. Michigan Math. J.,
50(1):71-87, 2002. [ bib | http ] |
| [184] | Stefanie Petermichl and
Alexander and Volberg. Heating
of the
Ahlfors-Beurling operator: weakly quasiregular maps on the plane are
quasiregular. Duke Math. J., 112(2):281-305, 2002. [ bib | http ] |
| [185] | S. Petermichl, S. Treil,
and A. Volberg. Why
the Riesz
transforms are averages of the dyadic shifts? Publ. Mat.,
(Vol. Extra):209-228, 2002. [ bib | http ] |
| [186] | F. Nazarov, , and
A. Volberg. The Bellman function,
the
two-weight Hilbert transform, and embeddings of the model spaces K
θ. J. Anal. Math., 87:385-414, 2002. [ bib | http ] |
| [187] | F. Nazarov, , G. Pisier,
S. Treil, and
A. Volberg.
Sharp estimates in vector Carleson imbedding theorem and for vector
paraproducts. J. Reine Angew. Math., 542:147-171, 2002. [ bib | http ] |
| [188] | Antonios D. Melas. On the
centered Hardy-Littlewood
maximal
operator. Trans. Amer. Math. Soc., 354(8):3263-3273
(electronic), 2002. [ bib | http ] |
| [189] | Tadeusz Iwaniec. Nonlinear
Cauchy-Riemann operators in R n. Trans. Amer.
Math. Soc., 354(5):1961-1995
(electronic),
2002. [ bib | http ] |
| [190] | Loukas Grafakos and Rodolfo H.
Torres. On multilinear
singular
integrals of Calderón-Zygmund type. Publ. Mat., (Vol.
Extra):57-91, 2002. [ bib | http ] |
| [191] | Loukas Grafakos and Rodolfo H.
Torres. Maximal operator
and
weighted norm inequalities for multilinear singular integrals. Indiana
Univ. Math. J., 51(5):1261-1276, 2002. [ bib | http ] |
| [192] | Liliana Forzani, Roberto Scotto,
Peter Sjögren, and
Wilfredo
Urbina. On the L p boundedness of the non-centered
Gaussian Hardy-Littlewood maximal function. Proc. Amer. Math. Soc.,
130(1):73-79 (electronic), 2002. [ bib | http ] |
| [193] | Claudia Capone, Luigi Greco, , and
Tadeusz Iwaniec. Higher
integrability via Riesz transforms and interpolation. Nonlinear
Anal., 49(4, Ser. A: Theory Methods):513-523, 2002. [ bib | http ] |
| [194] | Donald L. Burkholder. The best
constant in the Davis
inequality
for the expectation of the martingale square function. Trans.
Amer. Math. Soc., 354(1):91-105 (electronic), 2002. [ bib | http ] |
| [195] | Kari Astala and Daniel Faraco.
Quasiregular mappings and
Young
measures. Proc. Roy. Soc. Edinburgh Sect. A,
132(5):1045-1056, 2002. [ bib | http ] |
| [196] | Kari Astala, Mario Bonk, and Juha
Heinonen. Quasiconformal
mappings
with Sobolev boundary values. Ann. Sc. Norm. Super. Pisa Cl. Sci.
(5), 1(3):687-731, 2002. [ bib | http ] |
| [197] | Krzysztof Stempak and José
Luis and Torrea.
Poisson
integrals and Riesz transforms for Hermite function expansions with
weights. J. Funct. Anal., 202(2):443-472, 2003. [ bib | http ] |
| [198] | A. Volberg and F. and
Nazarov. Heat extension of
the Beurling
operator and estimates for its norm. Algebra i Analiz,
15(4):142-158, 2003. [ bib | http ] |
| [199] | Antonios D. Melas. The best
constant for the centered
Hardy-Littlewood maximal inequality. Ann. of Math. (2),
157(2):647-688, 2003. [ bib | http ] |
| [200] | E. Harboure, J. L. Torrea,
, and B. Viviani.
Vector-valued extensions of operators related to the Ornstein-Uhlenbeck
semigroup. J. Anal. Math., 91:1-29, 2003. [ bib | http ] |
| [201] | Loukas Grafakos and Terence Tao.
Multilinear interpolation
between
adjoint operators. J. Funct. Anal., 199(2):379-385, 2003. [ bib | http ] |
| [202] | Loukas Grafakos. Estimates for
maximal singular integrals. Colloq.
Math., 96(2):167-177, 2003. [ bib | http ] |
| [203] | L. Forzani,
R. Macías, and R. Scotto.
Pointwise
convergence of the Ornstein-Uhlenbeck semigroup. In Proceedings of
the Seventh ``Dr. Antonio A. R. Monteiro'' Congress of Mathematics
(Spanish), pages 101-114, Bahí a Blanca, 2003. Univ. Nac.
del Sur. [ bib | http ] |
| [204] | Oliver Dragicevic and
Alexander and Volberg. Sharp
estimate of the
Ahlfors-Beurling operator via averaging martingale transforms. Michigan
Math. J., 51(2):415-435, 2003. [ bib | http ] |
| [205] | R. Bañuelos and
P. J.
Méndez-Hernández.
Space-time Brownian motion and the Beurling-Ahlfors transform. Indiana
Univ. Math. J., 52(4):981-990, 2003. [ bib | http ] |
| [206] | Kari Astala and Vincenzo Nesi.
Composites and quasiconformal
mappings:
new optimal bounds in two dimensions. Calc. Var. Partial
Differential Equations, 18(4):335-355, 2003. [ bib | http ] |
| [207] | Teresa Martínez and
José L. and Torrea.
Boundedness
of vector-valued Martingale transforms on extreme points and
applications. J. Aust. Math. Soc., 76(2):207-221, 2004. [ bib | http ] |
| [208] | Prabhu Janakiraman. Best weak-type (p,p)
constants,
1<= p<= 2, for orthogonal harmonic functions and
martingales. Illinois J. Math., 48(3):909-921, 2004. [ bib | http ] |
| [209] | Prabhu Janakiraman. Weak-type
estimates for singular
integrals and the
Riesz transform. Indiana Univ. Math. J., 53(2):533-555, 2004. [ bib | http ] |
| [210] | E. Harboure,
L. de Rosa, C. Segovia, and
J. L. and Torrea. L p-dimension free
boundedness for Riesz transforms associated to Hermite functions. Math.
Ann., 328(4):653-682, 2004. [ bib | http ] |
| [211] | Loukas Grafakos, Terence Tao, and
Erin Terwilleger. L p
bounds for a maximal dyadic sum operator. Math. Z.,
246(1-2):321-337, 2004. [ bib | http ] |
| [212] | Loukas Grafakos and Xiaochun and
Li. Uniform bounds for
the
bilinear Hilbert transforms. I. Ann. of Math. (2),
159(3):889-933, 2004. [ bib | http ] |
| [213] | L. Grafakos. Classical and
Modern Fourier Analysis.
Pearson Education, Inc., New Jersey, 2004. [ bib ] |
| [214] | T. A. Gillespie and José
L. and Torrea.
Dimension free
estimates for the oscillation of Riesz transforms. Israel J. Math.,
141:125-144, 2004. [ bib | http ] |
| [215] | Jiyeon Suh. A sharp weak type (p,p)
inequality (p>2)
for martingale transforms and other subordinate martingales. Trans.
Amer. Math. Soc., 357(4):1545-1564 (electronic), 2005. [ bib | http ] |
| [216] | E. Harboure, R. A.
Macías, M. T.
Menárguez, and J. L. and Torrea. Oscillation and
variation for the Gaussian Riesz transforms and Poisson integral. Proc.
Roy. Soc. Edinburgh Sect. A, 135(1):85-104, 2005. [ bib | http ] |
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