The UMD property for musielak–orlicz spaces

Nick Lindemulder; Mark Veraar; Ivan Yaroslavtsev

doi:10.1007/978-3-030-10850-2_19

The UMD property for musielak–orlicz spaces

Nick Lindemulder, Mark Veraar^*, Ivan Yaroslavtsev

^*Corresponding author for this work

Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific

9 Citations (Scopus)

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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 L^p(·) are UMD spaces.

Original language	English
Title of host publication	Positivity and Noncommutative Analysis
Subtitle of host publication	Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday
Editors	G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven, A. Wickstead
Place of Publication	Cham
Publisher	Springer
Pages	349-363
Number of pages	15
ISBN (Electronic)	978-3-030-10850-2
ISBN (Print)	978-3-030-10849-6
DOIs	https://doi.org/10.1007/978-3-030-10850-2_19
Publication status	Published - 2019

Publication series

Name	Trends 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 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.

Keywords

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

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10.1007/978-3-030-10850-2_19

Lindemulder2019_Chapter_TheUMDPropertyForMusielakOrlicFinal published version, 357 KB

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Lindemulder, N., Veraar, M., & Yaroslavtsev, I. (2019). The UMD property for musielak–orlicz spaces. In G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven, & A. Wickstead (Eds.), Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday (pp. 349-363). (Trends in Mathematics). Springer. https://doi.org/10.1007/978-3-030-10850-2_19

Lindemulder, Nick ; Veraar, Mark ; Yaroslavtsev, Ivan. / The UMD property for musielak–orlicz spaces. Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday. editor / G. Buskes ; M. de Jeu ; P. Dodds ; A. Schep ; F. Sukochev ; J. van Neerven ; A. Wickstead. Cham : Springer, 2019. pp. 349-363 (Trends in Mathematics).

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Lindemulder, N , Veraar, M & Yaroslavtsev, I 2019, The UMD property for musielak–orlicz spaces. in G Buskes, M de Jeu, P Dodds, A Schep, F Sukochev, J van Neerven & A Wickstead (eds), Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday. Trends in Mathematics, Springer, Cham, pp. 349-363. https://doi.org/10.1007/978-3-030-10850-2_19

The UMD property for musielak–orlicz spaces. / Lindemulder, Nick ; Veraar, Mark; Yaroslavtsev, Ivan.
Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday. ed. / G. Buskes; M. de Jeu; P. Dodds; A. Schep; F. Sukochev; J. van Neerven; A. Wickstead. Cham: Springer, 2019. p. 349-363 (Trends in Mathematics).

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific

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T1 - The UMD property for musielak–orlicz spaces

AU - Lindemulder, Nick

AU - Veraar, Mark

AU - Yaroslavtsev, Ivan

N1 - 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.

PY - 2019

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N2 - 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.

AB - 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.

KW - Musielak–Orlicz spaces

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KW - Variable L-spaces

KW - Variable Lebesgue spaces

KW - Vector-valued martingales

KW - Young functions

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Lindemulder N , Veraar M, Yaroslavtsev I. The UMD property for musielak–orlicz spaces. In Buskes G, de Jeu M, Dodds P, Schep A, Sukochev F, van Neerven J, Wickstead A, editors, Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday. Cham: Springer. 2019. p. 349-363. (Trends in Mathematics). doi: 10.1007/978-3-030-10850-2_19

The UMD property for musielak–orlicz spaces

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Keywords

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