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arXiv · 2004.12712

On grand Sobolev spaces and pointwise description of Banach function spaces

Pankaj Jain·Anastasia Molchanova·Monika Singh·Sergey Vodopyanov
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Abstract

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study weighted grand Sobolev spaces, defined on arbitrary open sets (of finite or infinite measure), and provide pointwise description of them.

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Pankaj Jain, Anastasia Molchanova, Monika Singh, Sergey Vodopyanov. 2020-04-27. On grand Sobolev spaces and pointwise description of Banach function spaces. https://arxiv.org/abs/2004.12712

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