Vector-Valued Extensions of Operators Through Multilinear Limited Range Extrapolation

Emiel Lorist*, Bas Nieraeth

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
76 Downloads (Pure)


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
Issue number5
Publication statusPublished - 2019


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


Dive into the research topics of 'Vector-Valued Extensions of Operators Through Multilinear Limited Range Extrapolation'. Together they form a unique fingerprint.

Cite this