Multiplier theorems via martingale transforms

2020/03/04 by Bañuelos, Rodrigo, Baudoin, Fabrice, Chen, Li +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2003.02077

Abstract

We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp L^p bounds for second order Riesz transforms by a liming argument.

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