The UMD property for musielak–orlicz spaces

Book chapter (2019)

Authors

N. Lindemulder Analysis - EEMCS
M.C. Veraar Analysis - EEMCS
I.S. Yaroslavtsev Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2019 N. Lindemulder, M.C. Veraar, I.S. Yaroslavtsev
DOI: https://doi.org/10.1007/978-3-030-10850-2_19
UMD Musielak–Orlicz spaces Variable L-spaces Variable Lebesgue spaces Vector-valued martingales Young functions
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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.