Fourier multipliers in Banach function spaces with UMD concavifications
Functional Analysis
2019-08-08 v1 Classical Analysis and ODEs
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 -boundedness, which implies -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.
Cite
@article{arxiv.1705.07792,
title = {Fourier multipliers in Banach function spaces with UMD concavifications},
author = {Alex Amenta and Emiel Lorist and Mark Veraar},
journal= {arXiv preprint arXiv:1705.07792},
year = {2019}
}