Inhomogeneous Sobolev and Besov Spaces: Embeddings and prevalent smoothness
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911319387537408 |
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| author | Rible, Quentin |
| author_facet | Rible, Quentin |
| contents | In this article, we introduce inhomogeneous Sobolev spaces that naturally generalise the standard Sobolev-Slobodeckij spaces. The inhomogeneity of these spaces is governed by a set function $μ$, referred to as an environment. In the case where $μ$ is an almost doubling set function, we relate these new spaces with inhomogeneous Besov spaces recently introduced by Barral-Seuret in 2023. When $μ$ is in addition a capacity, wee also prove that prevalent elements in such spaces are multifractal (with a singularity spectrum that we determine), completing previous Baire generic results already obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inhomogeneous Sobolev and Besov Spaces: Embeddings and prevalent smoothness Rible, Quentin Classical Analysis and ODEs Functional Analysis In this article, we introduce inhomogeneous Sobolev spaces that naturally generalise the standard Sobolev-Slobodeckij spaces. The inhomogeneity of these spaces is governed by a set function $μ$, referred to as an environment. In the case where $μ$ is an almost doubling set function, we relate these new spaces with inhomogeneous Besov spaces recently introduced by Barral-Seuret in 2023. When $μ$ is in addition a capacity, wee also prove that prevalent elements in such spaces are multifractal (with a singularity spectrum that we determine), completing previous Baire generic results already obtained. |
| title | Inhomogeneous Sobolev and Besov Spaces: Embeddings and prevalent smoothness |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2512.13160 |