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.
Original language | English |
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Pages (from-to) | 1-32 |
Number of pages | 32 |
Journal | American Mathematical Society. Transactions |
DOIs | |
Publication status | E-pub ahead of print - 2018 |