Vector-Valued Extensions of Operators Through Multilinear Limited Range Extrapolation

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Abstract

We give an extension of Rubio de Francia’s extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an m-(sub)linear operator T:Lp1(w1p1)×⋯×Lpm(wmpm)→Lp(wp) for a certain class of Muckenhoupt weights yields an extension of the operator to Bochner spaces L p (w p ; X) for a wide class of Banach function spaces X, which includes certain Lebesgue, Lorentz and Orlicz spaces. We apply the extrapolation result to various operators, which yields new vector-valued bounds. Our examples include the bilinear Hilbert transform, certain Fourier multipliers and various operators satisfying sparse domination results.

Original languageEnglish
Pages (from-to)2608-2634
Number of pages27
JournalJournal of Fourier Analysis and Applications
Volume25
Issue number5
DOIs
Publication statusPublished - 2019

Keywords

  • Banach function space
  • Bilinear Hilbert transform
  • Extrapolation
  • Fourier multipliers
  • Limited range
  • Muckenhoupt weights
  • Multilinear
  • p-convexity
  • Sparse domination
  • UMD

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