Lipschitz spaces over non-porous sets
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912966625984512 |
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| author | Aliaga, Ramón J. |
| author_facet | Aliaga, Ramón J. |
| contents | Let $M$ be a subset of $\mathbb{R}^n$. If $M$ is not porous, in particular if it has positive $n$-dimensional Lebesgue measure, we prove that the Lipschitz spaces $\mathrm{Lip}_0(M)$ and $\mathrm{Lip}_0(\mathbb{R}^n)$ are linearly isomorphic. The result also holds more generally if $\mathbb{R}^n$ is replaced with a Carnot group equipped with its Carnot-Carathéodory metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz spaces over non-porous sets Aliaga, Ramón J. Functional Analysis 46E15, 46B03, 53C17 Let $M$ be a subset of $\mathbb{R}^n$. If $M$ is not porous, in particular if it has positive $n$-dimensional Lebesgue measure, we prove that the Lipschitz spaces $\mathrm{Lip}_0(M)$ and $\mathrm{Lip}_0(\mathbb{R}^n)$ are linearly isomorphic. The result also holds more generally if $\mathbb{R}^n$ is replaced with a Carnot group equipped with its Carnot-Carathéodory metric. |
| title | Lipschitz spaces over non-porous sets |
| topic | Functional Analysis 46E15, 46B03, 53C17 |
| url | https://arxiv.org/abs/2507.12119 |