Multiplier theorems via martingale transforms

Rodrigo Bañuelos*, Fabrice Baudoin, Li Chen, Yannick Sire

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

2 Citations (Scopus)

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 languageEnglish
Article number109188
JournalJournal of Functional Analysis
Volume281
Issue9
ISSN0022-1236
DOIs
Publication statusPublished - 1 Nov 2021
Externally publishedYes

Keywords

  • Martingale transforms
  • Multipliers
  • Universal bounds

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