Sobolev homeomorphisms and composition operators on homogeneous Lie groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908529293524992 |
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| author | Ukhlov, Alexander |
| author_facet | Ukhlov, Alexander |
| contents | In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism $φ: Ω\to\widetildeΩ$ belongs to the Sobolev space $L^{1}_{q}(Ω; \widetildeΩ)$, $1\leq q < \infty$, if and only if $φ$ generates a bounded composition operator on Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sobolev homeomorphisms and composition operators on homogeneous Lie groups Ukhlov, Alexander Analysis of PDEs 46E35, 22E30 In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism $φ: Ω\to\widetildeΩ$ belongs to the Sobolev space $L^{1}_{q}(Ω; \widetildeΩ)$, $1\leq q < \infty$, if and only if $φ$ generates a bounded composition operator on Sobolev spaces. |
| title | Sobolev homeomorphisms and composition operators on homogeneous Lie groups |
| topic | Analysis of PDEs 46E35, 22E30 |
| url | https://arxiv.org/abs/2504.11030 |