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The UMD property for musielak–orlicz spaces

Book Chapter (2019)
Author(s)

Nick Lindemulder (TU Delft - Analysis)

Mark Veraar (TU Delft - Analysis)

Ivan Yaroslavtsev (TU Delft - Analysis)

Research Group
Analysis
DOI related publication
https://doi.org/10.1007/978-3-030-10850-2_19
More Info
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Publication Year
2019
Language
English
Research Group
Analysis
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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. @en
Pages (from-to)
349-363
Publisher
Springer
ISBN (print)
978-3-030-10849-6
ISBN (electronic)
978-3-030-10850-2
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

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.

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