Rodrigo Banuelos (Purdue)

Sharp L^p-estimates for Fourier multipliers arising from Levy processes

Abstract:
We shall discuss some recent applications of the sharp martingale inequalities of Burkholder to various Fourier multipliers that arise from transformations of L\'evy processes via the L\'evy--Khintchine formula. While these results are of interest on their own right, they are motivated by a conjecture of T. Iwaniec on the L^p-norm of the Beurling-Ahlfors operator and its connections to rank-one convexity and quasiconvexity.