The UMD property for Musielak--Orlicz spaces
| Autor: | Lindemulder, Nick, Veraar, Mark, Yaroslavtsev, Ivan |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: minor revision |
| Databáze: | arXiv |
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