The UMD property for musielak–orlicz spaces

Nick Lindemulder, Mark Veraar*, Ivan Yaroslavtsev

*Corresponding author for this work

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

7 Citations (Scopus)
16 Downloads (Pure)


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
Number of pages15
ISBN (Electronic)978-3-030-10850-2
ISBN (Print)978-3-030-10849-6
Publication statusPublished - 2019

Publication series

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

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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


Dive into the research topics of 'The UMD property for musielak–orlicz spaces'. Together they form a unique fingerprint.

Cite this