The UMD property for musielak–orlicz spaces

Nick Lindemulder, Mark Veraar, Ivan Yaroslavtsev

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific

4 Citations (Scopus)
11 Downloads (Pure)

Abstract

In this paper we show that Musielak–Orlicz spaces are UMD spaces under the so-called Δ2 condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak–Orlicz space has the UMD property if and only if it is reflexive. As a consequence we show that reflexive variable Lebesgue spaces Lp(·) are UMD spaces.

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, A. Wickstead
Place of PublicationCham
PublisherSpringer
Pages349-363
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

  • Musielak–Orlicz spaces
  • UMD
  • Variable L-spaces
  • Variable Lebesgue spaces
  • Vector-valued martingales
  • Young functions

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