Rescaled extrapolation for vector-valued functions

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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.

Original languageEnglish
Pages (from-to)155-182
Number of pages28
JournalPublicacions Matematiques
Volume63
Issue number1
DOIs
Publication statusPublished - 2019

Keywords

  • Banach function spaces
  • Extrapolation
  • Fourier multipliers
  • Hardy-Littlewood maximal function
  • Littlewood-Paley-Rubio de Francia inequalities
  • Muckenhoupt weights
  • P-convexity
  • UMD
  • Variational Carleson operator

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