Fourier Multipliers in Banach Function Spaces with UMD Concavifications

Journal article (2018)

Authors

Alex Amenta Analysis - EEMCS
E. Lorist Analysis - EEMCS
M.C. Veraar Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2018 Alex Amenta, E. Lorist, M.C. Veraar
DOI: https://doi.org/10.1090/tran/7520
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call $ {\ell ^{r}(\ell ^{s})}$-boundedness, which implies $ \mathcal {R}$-boundedness in many cases. The proofs are based on new Littlewood-Paley-Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors.

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