The ℓ s-boundedness of a family of integral operators on UMD banach function spaces

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Abstract

We prove the ℓs-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the ℓs-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of ℓs-boundedness as weighted boundedness by Rubio de Francia.

Original languageEnglish
Title of host publicationPositivity and Noncommutative Analysis
Subtitle of host publicationFestschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday
EditorsG. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven
Place of PublicationCham
PublisherBirkhäuser
Pages365-379
Number of pages15
ISBN (Electronic)978-3-030-10850-2
ISBN (Print)978-3-030-10849-6
DOIs
Publication statusPublished - 2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Keywords

  • Banach function space
  • Hardy–Littlewood maximal operator
  • Integral operator
  • Muckenhoupt weights
  • UMD
  • ℓ-boundedness

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