Jain, P., Molchanova, A., Singh, M., & Vodopyanov, S. (2021). On grand Sobolev spaces and pointwise description of Banach function spaces. Nonlinear Analysis: Theory, Methods and Applications, 202(112100), 112100. https://doi.org/10.1016/j.na.2020.112100
Nonlinear Analysis: Theory, Methods and Applications
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ISSN:
0362-546X
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Date (published):
2021
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Number of Pages:
17
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Peer reviewed:
Yes
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Keywords:
Applied Mathematics; Analysis; Banach function space; Grand Sobolev space; Maximal function; Pointwise description
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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.
