Fourier Multipliers in Banach Function Spaces with UMD Concavifications

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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.
Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalAmerican Mathematical Society. Transactions
Publication statusE-pub ahead of print - 2018

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