Multiplier theorems via martingale transforms
Document Type
Article
Publication Date
3-4-2020
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.
Recommended Citation
Chen, L. (2020). Multiplier theorems via martingale transforms. Retrieved from https://repository.lsu.edu/mathematics_pubs/1391