Multiplier theorems via martingale transforms
Probability
2021-07-13 v2 Analysis of PDEs
Functional Analysis
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 bounds for second order Riesz transforms by a liming argument.
Cite
@article{arxiv.2003.02077,
title = {Multiplier theorems via martingale transforms},
author = {Rodrigo Bañuelos and Fabrice Baudoin and Li Chen and Yannick Sire},
journal= {arXiv preprint arXiv:2003.02077},
year = {2021}
}
Comments
The paper generalizes results and extends the framework and scope of the paper arXiv:1802.02410