Functional inequalities: the Hardy-Littlewood-Sobolev inequality and log Sobolev inequality.

Levy processes, the fractional Laplacian, non-local operators and related PDEs.

1. Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups, Potential Anal. (2016), pp.1–13
[article]
[arXiv]

2. (with Rodrigo Bañuelos) On square functions and Fourier multipliers for nonlocal operators, summitted, arXiv preprint (2017)
[arXiv]

1. Probability seminar, Purdue University, February 2016
[slide]

2. Seminar on Stochastic processes, University of Maryland, March 2016 (short talk session)

3. Probability seminar, UIUC, March 2017
[slide]

4. Probability seminar, Purdue University, September 2017