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arXiv · 2307.16291

Sobolev meets Riesz: a characterization of weighted Sobolev spaces via weighted Riesz bounded variation space

David Cruz-Uribe·Oscar Guzman·Humberro Rafeiro
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Abstract

We introduce weighted Riesz bounded variation spaces defined on an open subset of the $n$-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia's extrapolation theory, a similar characterization of the variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces is obtained.

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David Cruz-Uribe, Oscar Guzman, Humberro Rafeiro. 2023-07-30. Sobolev meets Riesz: a characterization of weighted Sobolev spaces via weighted Riesz bounded variation space. https://arxiv.org/abs/2307.16291

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