Multiplier theorems via martingale transforms

Rodrigo Bañuelos; Fabrice Baudoin; Li Chen; Yannick Sire

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arXiv · 2003.02077

Multiplier theorems via martingale transforms

Rodrigo Bañuelos·Fabrice Baudoin·Li Chen·Yannick Sire

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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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BibTeX RIS

Rodrigo Bañuelos, Fabrice Baudoin, Li Chen, Yannick Sire. 2020-03-04. Multiplier theorems via martingale transforms. https://arxiv.org/abs/2003.02077

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