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arXiv · 1810.13362

The UMD property for Musielak--Orlicz spaces

Nick Lindemulder·Mark Veraar·Ivan Yaroslavtsev
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Abstract

In this paper we show that Musielak--Orlicz spaces are UMD spaces under the so-called $\Delta_2$ 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 $L^{p(\cdot)}$ are UMD spaces.

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Nick Lindemulder, Mark Veraar, Ivan Yaroslavtsev. 2018-10-31. The UMD property for Musielak--Orlicz spaces. https://arxiv.org/abs/1810.13362

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