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
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
2. Seminar on Stochastic processes, University of Maryland, March 2016 (short talk session)
3. Probability seminar, UIUC, March 2017 [slide]