Rodrigo Banuelos (Purdue)

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

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.