Rodrigo Bañuelos


My research has been partially supported by the National Science Foundation,
1986-present.  I gratefully acknowledge this support


[1] Rodrigo Bañuelos and Daesung Kim. Hardy-Stein identity for non-symmetric Lévy processes and Fourier multipliers.
J. Math. Anal. Appl., 480(1):123383, 20, 2019. [ bib | DOI | http ]
[2] Rodrigo Bañuelos and Mateusz Kwaśnicki. On the Lp-norm of the discrete Hilbert transform.
Duke Math. J.
, 168(3):471--504, 2019. [ bib | DOI | http ]
[3] Rodrigo Bañuelos and Adam Os ekowski. Stability in Burkholder's differentially subordinate martingales inequalities
 and applications to Fourier multipliers. J. Math. Pures Appl. (9), 119:1--44, 2018. [ bib | DOI | http ]
[4] Rodrigo Bañuelos and Adam Os ekowski. A weighted maximal inequality for differentially subordinate martingales.
Proc. Amer. Math. Soc., 146(5):2263--2275, 2018. [ bib | DOI | http ]
[5] Rodrigo Bañuelos and Adam Osekowski. Weighted L2 inequalities for square functions.
Trans. Amer. Math. Soc.
, 370(4):2391--2422, 2018. [ bib | DOI | http ]
[6] Rodrigo Bañuelos and Adam Osekowski. Sharp weak type inequalities for fractional integral operators.
Potential Anal., 47(1):103--121, 2017. [ bib | DOI | http ]
[7] Rodrigo Bañuelos and Burgess Davis. Introduction to memorial issue for Donald Burkholder (1927--2013).
 Ann. Probab., 45(1):1--3, 2017. [ bib | DOI | http ]
[8] Rodrigo Bañuelos, Krzysztof Bogdan, and Tomasz Luks. Hardy-Stein identities and square functions for semigroups.
J. Lond. Math. Soc. (2)
, 94(2):462--478, 2016. [ bib | DOI | http ]
[9] Rodrigo Bañuelos and Adam Osekowski. On Astala's theorem for martingales and Fourier multipliers.
Adv. Math.
, 283:275--302, 2015. [ bib | DOI | http ]
[10] Rodrigo Bañuelos and Adam Osekowski. Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space.
J. Funct. Anal., 269(6):1652--1713, 2015. [ bib | DOI | http ]
[11] Rodrigo Bañuelos and Adam Osekowski. Weighted norm inequalities for fractional maximal operators: a Bellman function approach.
 Indiana Univ. Math. J., 64(3):957--972, 2015. [ bib | DOI | http ]
[12] David Applebaum and Rodrigo Bañuelos. Probabilistic approach to fractional integrals and the Hardy-Littlewood-Sobolev inequality.
In Analytic methods in interdisciplinary applications, volume 116 of Springer Proc.
Math. Stat.
, pages 17--40. Springer, Cham, 2015. [ bib | DOI | http ]
[13] Rodrigo Bañuelos and Dante DeBlassie. On the first eigenfunction of the symmetric stable process in a bounded Lipschitz domain.
Potential Anal., 42(2):573--583, 2015. [ bib | DOI | http ]
[14] Luis Acuña Valverde and Rodrigo Bañuelos. Heat content and small time asymptotics for Schrödinger operators on Rd.
Potential Anal., 42(2):457--482, 2015. [ bib | DOI | http ]
[15] Rodrigo Bañuelos and Adam Osekowski. Sharp maximal Lp-estimates for martingales.
Illinois J. Math.
, 58(1):149--165, 2014. [ bib | http ]
[16] Rodrigo Bañuelos and Adam Osekowski. On the Bellman function of Nazarov, Treil and Volberg.
 Math. Z., 278(1-2):385--399, 2014. [ bib | DOI | http ]
[17] David Applebaum and Rodrigo Bañuelos. Martingale transform and Lévy processes on Lie groups.
Indiana Univ. Math. J.
, 63(4):1109--1138, 2014. [ bib | DOI | http ]
[18] Rodrigo Bañuelos and Adam Osekowski. On the operator Λ* and the Beurling-Ahlfors transform on radial functions.
Michigan Math. J.
, 63(1):213--221, 2014. [ bib | DOI | http ]
[19] Rodrigo Bañuelos, Jebessa B. Mijena, and Erkan Nane. Two-term trace estimates for relativistic stable processes.
J. Math. Anal. Appl., 410(2):837--846, 2014. [ bib | DOI | http ]
[20] Rodrigo Bañuelos and Adam Osekowski. Burkholder inequalities for submartingales, Bessel processes and conformal martingales.
Amer. J. Math., 135(6):1675--1698, 2013. [ bib | DOI | http ]
[21] Rodrigo Bañuelos and Fabrice Baudoin. Martingale transforms and their projection operators on manifolds.
Potential Anal.
, 38(4):1071--1089, 2013. [ bib | DOI | http ]
[22] Rodrigo Bañuelos and Selma Yildiri m Yolcu. Heat trace of non-local operators.
J. Lond. Math. Soc. (2)
, 87(1):304--318, 2013. [ bib | DOI | http ]
[23] Rodrigo Bañuelos and Adam Osekowski. Sharp inequalities for the Beurling-Ahlfors transform on radial functions.
Duke Math. J.
, 162(2):417--434, 2013. [ bib | DOI | http ]
[24] Rodrigo Bañuelos and Adam Osekowski. Martingales and sharp bounds for Fourier multipliers.
 Ann. Acad. Sci. Fenn. Math., 37(1):251--263, 2012. [ bib | DOI | http ]
[25] Rodrigo Bañuelos, Adam Bielaszewski, and Krzysztof Bogdan. Fourier multipliers for non-symmetric Lévy processes.
In Marcinkiewicz centenary volume, volume 95 of Banach Center Publ., pages 9--25.
Polish Acad. Sci. Inst. Math., Warsaw, 2011. [ bib | DOI | http ]
[26] Rodrigo Bañuelos and Tom Carroll. The maximal expected lifetime of Brownian motion.
Math. Proc. R. Ir. Acad., 111A(1):1--11, 2011. [ bib | DOI | http ]
[27] Rodrigo Bañuelos. The foundational inequalities of D. L. Burkholder and some of their ramifications.
Illinois J. Math.
, 54(3):789--868 (2012), 2010. [ bib | http ]
[28] Rodrigo Bañuelos, Tadeusz Kulczycki, Iosif Polterovich, and Bartl omiej Siudeja. Eigenvalue inequalities for mixed Steklov problems.
 In Operator theory and its applications, volume 231 of Amer. Math. Soc. Transl. Ser. 2, pages 19--34.
Amer. Math. Soc., Providence, RI, 2010. [ bib | DOI | http ]
[29] Rodrigo Bañuelos and Tom Carroll. Stretching convex domains and the hyperbolic metric.
Q. J. Math., 61(3):265--273, 2010. [ bib | DOI | http ]
[30] Rodrigo Bañuelos and Pedro J. Méndez-Hernández. Symmetrization of Lévy processes and applications.
J. Funct. Anal., 258(12):4026--4051, 2010. [ bib | DOI | http ]
[31] Rodrigo Bañuelos and Prabhu Janakiraman. On the weak-type constant of the Beurling-Ahlfors transform.
Michigan Math. J.
, 58(2):459--477, 2009. [ bib | DOI | http ]
[32] Rodrigo Bañuelos, Tadeusz Kulczycki, and Bartl omiej Siudeja. On the trace of symmetric stable processes on Lipschitz domains.
J. Funct. Anal., 257(10):3329--3352, 2009. [ bib | DOI | http ]
[33] R. Bañuelos, T. Kulczycki, and B. Siudeja. Neumann Bessel heat kernel monotonicity.
 Potential Anal., 30(1):65--83, 2009. [ bib | DOI | http ]
[34] Rodrigo Bañuelos and Michael M. H. Pang. Stability and approximations of eigenvalues and eigenfunctions for the Neumann Laplacian.
I. Electron. J. Differential Equations, pages No. 145, 13, 2008. [ bib ]
[35] Rodrigo Bañuelos and Tadeusz Kulczycki. Trace estimates for stable processes.
 Probab. Theory Related Fields, 142(3-4):313--338, 2008. [ bib | DOI | http ]
[36] Rodrigo Bañuelos and Prabhu Janakiraman. Lp-bounds for the Beurling-Ahlfors transform.
Trans. Amer. Math. Soc.
, 360(7):3603--3612, 2008. [ bib | DOI | http ]
[37] Rodrigo Bañuelos and Krzysztof Bogdan. Lévy processes and Fourier multipliers.
J. Funct. Anal.
, 250(1):197--213, 2007. [ bib | DOI | http ]
[38] Rodrigo Bañuelos and Tadeusz Kulczycki. Spectral gap for the Cauchy process on convex, symmetric domains.
Comm. Partial Differential Equations, 31(10-12):1841--1878, 2006. [ bib | DOI | http ]
[39] Rodrigo Bañuelos and Pedro J. Méndez-Hernández. Hot-spots for conditioned Brownian motion.
Illinois J. Math.
, 50(1-4):1--32, 2006. [ bib | http ]
[40] Rodrigo Bañuelos and Michael M. H. Pang. Level sets of Neumann eigenfunctions.
Indiana Univ. Math. J., 55(3):923--939, 2006. [ bib | DOI | http ]
[41] Rodrigo Bañuelos, Tadeusz Kulczycki, and Pedro J. Méndez-Hernández. On the shape of the ground state eigenfunction for stable processes.
Potential Anal.
, 24(3):205--221, 2006. [ bib | DOI | http ]
[42] Rodrigo Bañuelos and Tadeusz Kulczycki. Eigenvalue gaps for the Cauchy process and a Poincaré inequality.
J. Funct. Anal.
, 234(1):199--225, 2006. [ bib | DOI | http ]
[43] Rodrigo Bañuelos and Dante DeBlassie. The exit distribution of iterated Brownian motion in cones.
Stochastic Process. Appl., 116(1):36--69, 2006. [ bib | DOI | http ]
[44] Rodrigo Bañuelos and Krzysztof Bogdan. Symmetric stable processes in parabola-shaped regions.
 Proc. Amer. Math. Soc., 133(12):3581--3587, 2005. [ bib | DOI | http ]
[45] Rodrigo Bañuelos and Tom Carroll. Sharp integrability for Brownian motion in parabola-shaped regions.
 J. Funct. Anal., 218(1):219--253, 2005. [ bib | DOI | http ]
[46] Rodrigo Bañuelos, Michael Pang, and Mihai Pascu. Brownian motion with killing and reflection and the “hot-spots” problem.
Probab. Theory Related Fields, 130(1):56--68, 2004. [ bib | DOI | http ]
[47] Rodrigo Bañuelos and Krzysztof Bogdan. Symmetric stable processes in cones. Potential Anal., 21(3):263--288, 2004. [ bib | DOI | http ]
[48] Rodrigo Bañuelos and Tadeusz Kulczycki. The Cauchy process and the Steklov problem.
 J. Funct. Anal., 211(2):355--423, 2004. [ bib | DOI | http ]
[49] Rodrigo Bañuelos and Michael Pang. An inequality for potentials and the “hot-spots” conjecture.
Indiana Univ. Math. J.
, 53(1):35--47, 2004. [ bib | DOI | http ]
[50] 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 | DOI | http ]
[51] Rodrigo Bañuelos, M. van den Berg, and Tom Carroll. Torsional rigidity and expected lifetime of Brownian motion.
J. London Math. Soc. (2), 66(2):499--512, 2002. [ bib | DOI | http ]
[52] Rodrigo Bañuelos and Pawel Kröger. Gradient estimates for the ground state Schrödinger eigenfunction and applications.
Comm. Math. Phys.
, 224(2):545--550, 2001. [ bib | DOI | http ]
[53] Rodrigo Bañuelos, R. Dante DeBlassie, and Robert Smits. The first exit time of planar Brownian motion from the interior of a parabola.
 Ann. Probab., 29(2):882--901, 2001. [ bib | DOI | http ]
[54] Rodrigo Bañuelos, RafalLatal a, and Pedro J. Méndez-Hernández. A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes.
Proc. Amer. Math. Soc.
, 129(10):2997--3008, 2001. [ bib | DOI | http ]
[55] R. Bañuelos and T. Carroll. Extremal problems for conditioned Brownian motion and the hyperbolic metric.
Ann. Inst. Fourier (Grenoble)
, 50(5):1507--1532, 2000. [ bib | http ]
[56] Rodrigo Bañuelos and Pedro J. Méndez-Hernández. Sharp inequalities for heat kernels of Schrödinger operators and applications to spectral gaps.
J. Funct. Anal., 176(2):368--399, 2000. [ bib | DOI | http ]
[57] Rodrigo Bañuelos and Gang Wang. Davis's inequality for orthogonal martingales under differential subordination. Michigan Math.
J.
, 47(1):109--124, 2000. [ bib | DOI | http ]
[58] Rodrigo Bañuelos and Charles N. Moore. Probabilistic behavior of harmonic functions, volume 175 of Progress in Mathematics.
Birkhäuser Verlag, Basel, 1999. [ bib | DOI | http ]
[59] Rodrigo Bañuelos and Krzysztof Burdzy. On the “hot spots” conjecture of J. Rauch.
 J. Funct. Anal., 164(1):1--33, 1999. [ bib | DOI | http ]
[60] Rodrigo Bañuelos and Michael M. H. Pang. Lower bound gradient estimates for solutions of Schrödinger equations and heat kernels.
Comm. Partial Differential Equations, 24(3-4):499--543, 1999. [ bib | DOI | http ]
[61] Rodrigo Bañuelos, Tom Carroll, and Elizabeth Housworth. Inradius and integral means for Green's functions and conformal mappings.
Proc. Amer. Math. Soc.
, 126(2):577--585, 1998. [ bib | DOI | http ]
[62] Rodrigo Bañuelos and Robert G. Smits. Brownian motion in cones.
Probab. Theory Related Fields
, 108(3):299--319, 1997. [ bib | DOI | http ]
[63] Rodrigo Bañuelos and Pawel Kröger. Isoperimetric-type bounds for solutions of the heat equation. Indiana Univ. Math. J., 46(1):83--91, 1997. [ bib | DOI | http ]
[64] Rodrigo Bañuelos and Arthur Lindeman, II. A martingale study of the Beurling-Ahlfors transform in Rn.
J. Funct. Anal., 145(1):224--265, 1997. [ bib | DOI | http ]
[65] Rodrigo Bañuelos and Gang Wang. Orthogonal martingales under differential subordination and applications to Riesz transforms.
Illinois J. Math., 40(4):678--691, 1996. [ bib | http ]
[66] R. Bañuelos and M. van den Berg. Dirichlet eigenfunctions for horn-shaped regions and Laplacians on cross sections.
J. London Math. Soc. (2)
, 53(3):503--511, 1996. [ bib | DOI | http ]
[67] Rodrigo Bañuelos and Tom Carroll. Addendum to: “Brownian motion and the fundamental frequency of a drum”
[Duke Math. J. 75 (1994), no. 3, 575--602; MR1291697 (96m:31003)]. Duke Math. J., 82(1):227, 1996. [ bib | DOI | http ]
[68] R. Bañuelos. Sharp estimates for Dirichlet eigenfunctions in simply connected domains.
J. Differential Equations
, 125(1):282--298, 1996. [ bib | DOI | http ]
[69] Rodrigo Bañuelos and Gang Wang. Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms.
Duke Math. J.
, 80(3):575--600, 1995. [ bib | DOI | http ]
[70] Rodrigo Bañuelos and Antônio Sá Barreto. On the heat trace of Schrödinger operators.
Comm. Partial Differential Equations, 20(11-12):2153--2164, 1995. [ bib | DOI | http ]
[71] Rodrigo Bañuelos and Elizabeth Housworth. An isoperimetric-type inequality for integrals of Green's functions.
Michigan Math. J., 42(3):603--611, 1995. [ bib | DOI | http ]
[72] Rodrigo Bañuelos and Tom Carroll. An improvement of the Osserman constant for the bass note of a drum.
In Stochastic analysis (Ithaca, NY, 1993), volume 57 of Proc. Sympos. Pure Math., pages 3--10. Amer. Math. Soc., Providence, RI, 1995. [ bib | DOI | http ]
[73] Rodrigo Bañuelos and Tom Carroll. Brownian motion and the fundamental frequency of a drum.
Duke Math. J., 75(3):575--602, 1994. [ bib | DOI | http ]
[74] Rodrigo Bañuelos and Burgess Davis. Erratum: “Sharp estimates for Dirichlet eigenfunctions in horn-shaped regions”
[Comm. Math. Phys. 150 (1992), no. 1, 209--215; MR1188505 (93i:35020)]. Comm. Math. Phys., 162(1):215--216, 1994. [ bib | http ]
[75] Rodrigo Bañuelos and Jean Brossard. The area integral and its density for BMO and VMO functions.
 Ark. Mat., 31(2):175--196, 1993. [ bib | DOI | http ]
[76] Rodrigo Bañuelos and Tom Carroll. Conditioned Brownian motion and hyperbolic geodesics in simply connected domains.
Michigan Math. J., 40(2):321--332, 1993. [ bib | DOI | http ]
[77] Rodrigo Bañuelos and Burgess Davis. A geometrical characterization of intrinsic ultracontractivity for planar domains with boundaries given by the graphs of functions. Indiana Univ. Math. J., 41(4):885--913, 1992. [ bib | DOI | http ]
[78] Rodrigo Bañuelos and Burgess Davis. Sharp estimates for Dirichlet eigenfunctions in horn-shaped regions.
Comm. Math. Phys., 150(1):209--215, 1992. [ bib | http ]
[79] Rodrigo Bañuelos. Lifetime and heat kernel estimates in nonsmooth domains. In Partial differential equations with minimal smoothness and applications (Chicago, IL, 1990), volume 42 of IMA Vol. Math. Appl., pages 37--48. Springer, New York, 1992. [ bib | DOI | http ]
[80] Rodrigo Bañuelos, Richard F. Bass, and Krzysztof Burdzy. Hölder domains and the boundary Harnack principle.
Duke Math. J.
, 64(1):195--200, 1991. [ bib | DOI | http ]
[81] Rodrigo Bañuelos. Intrinsic ultracontractivity and eigenfunction estimates for Schrödinger operators.
J. Funct. Anal.
, 100(1):181--206, 1991. [ bib | DOI | http ]
[82] R. Bañuelos and Ch. N. Moore. Distribution function inequalities for the density of the area integral.
Ann. Inst. Fourier (Grenoble)
, 41(1):137--171, 1991. [ bib | http ]
[83] Rodrigo Bañuelos and Charles N. Moore. Mean growth of Bloch functions and Makarov's law of the iterated logarithm.
Proc. Amer. Math. Soc.
, 112(3):851--854, 1991. [ bib | DOI | http ]
[84] R. Bañuelos, I. Klemes, and C. Moore. The lower bound in the law of the iterated logarithm for harmonic functions.
Duke Math. J., 60(3):689--715, 1990. [ bib | DOI | http ]
[85] Rodrigo Bañuelos, Richard F. Bass, and Krzysztof Burdzy. A representation of local time for Lipschitz surfaces.
Probab. Theory Related Fields, 84(4):521--547, 1990. [ bib | DOI | http ]
[86] Rodrigo Bañuelos and Charles N. Moore. Some results in analysis related to the law of the iterated logarithm.
In Analysis at Urbana, Vol. I (Urbana, IL, 1986--1987), volume 137 of London Math. Soc. Lecture Note Ser.,
pages 47--80. Cambridge Univ. Press, Cambridge, 1989. [ bib ]
[87] Rodrigo Bañuelos and Burgess Davis. Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains.
J. Funct. Anal., 84(1):188--200, 1989. [ bib | DOI | http ]
[88] Rodrigo Bañuelos and Charles N. Moore. Laws of the iterated logarithm, sharp good-λ inequalities and Lp-estimates for caloric and harmonic functions. Indiana Univ. Math. J., 38(2):315--344, 1989. [ bib | DOI | http ]
[89] Rodrigo Bañuelos and Charles N. Moore. Sharp estimates for the nontangential maximal function and the Lusin area function in Lipschitz domains.
Trans. Amer. Math. Soc., 312(2):641--662, 1989. [ bib | DOI | http ]
[90] Rodrigo Bañuelos and Andrew G. Bennett. Paraproducts and commutators of martingale transforms.
Proc. Amer. Math. Soc.
, 103(4):1226--1234, 1988. [ bib | DOI | http ]
[91] Rodrigo Bañuelos, Ivo Klemes, and Charles N. Moore. An analogue for harmonic functions of Kolmogorov's law of the iterated logarithm.
Duke Math. J.
, 57(1):37--68, 1988. [ bib | DOI | http ]
[92] Rodrigo Bañuelos. A sharp good-λ inequality with an application to Riesz transforms.
Michigan Math. J.
, 35(1):117--125, 1988. [ bib | DOI | http ]
[93] Rodrigo Bañuelos. On an estimate of Cranston and McConnell for elliptic diffusions in uniform domains.
Probab. Theory Related Fields, 76(3):311--323, 1987. [ bib | DOI | http ]
[94] R. Bañuelos and B. Ø ksendal. Exit times for elliptic diffusions and BMO.
Proc. Edinburgh Math. Soc. (2), 30(2):273--287, 1987. [ bib | DOI | http ]
[95] Rodrigo Bañuelos. A note on martingale transforms and Ap-weights. Studia Math., 85(2):125--135, 1987. [ bib | DOI | http ]
[96] Rodrigo Bañuelos and Bernt Ø ksendal. A stochastic approach to quasi-everywhere boundary convergence of harmonic functions.
J. Funct. Anal., 72(1):13--27, 1987. [ bib | DOI | http ]
[97] Rodrigo Bañuelos. Brownian motion and area functions. Indiana Univ. Math. J., 35(3):643--668, 1986. [ bib | DOI | http ]
[98] Rodrigo Bañuelos. Martingale transforms and related singular integrals.
Trans. Amer. Math. Soc.
, 293(2):547--563, 1986. [ bib | DOI | http ]
[99] R. Bañuelos and T. Wolff. Note on H2 on planar domains.
 Proc. Amer. Math. Soc., 95(2):217--218, 1985. [ bib | DOI | http ]
[100] Rodrigo Banuelos. MARTINGALE TRANSFORMS, RELATED SINGULAR INTEGRALS, AND A(,P)-WEIGHTS.
ProQuest LLC, Ann Arbor, MI, 1984. Thesis (Ph.D.)--University of California, Los Angeles. [ bib | http ]

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