# Fourier Multipliers in Banach Function Spaces with UMD Concavifications

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3 Citations (Scopus)
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.