Rescaled extrapolation for vector-valued functions

Abstract

We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.

arXiv commentAssumption on well-definedness and strong measurability added to main theorems. Minor modifications. To appear in Publicacions Matematiques

References in corpus (5)

• On the ${\ell }^s$-boundedness of a family of integral operators
• The local non-homogeneous Tb theorem for vector-valued functions
• $\gamma$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces
• Vector Valued Transference
• Maximal Regularity: Positive Counterexamples on UMD-Banach Lattices and Exact Intervals for the Negative Solution of the Extrapolation Problem

Cited by in corpus (7)

• Extrapolation in general quasi-Banach function spaces
• Euclidean structures and operator theory in Banach spaces
• Sparse domination implies vector-valued sparse domination
• Off-diagonal estimates for bi-commutators
• Vector-valued extensions of operators through multilinear limited range extrapolation
• Multi-parameter estimates via operator-valued shifts
• The ${\ell }^s$-boundedness of a family of integral operators on UMD Banach function spaces