Abstract
We develop a new and general 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 Lp bounds for second order Riesz transforms by a limiting argument.
Original language | English |
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Article number | 109188 |
Journal | Journal of Functional Analysis |
Volume | 281 |
Issue | 9 |
ISSN | 0022-1236 |
DOIs | |
Publication status | Published - 1 Nov 2021 |
Externally published | Yes |
Keywords
- Martingale transforms
- Multipliers
- Universal bounds