Sobolev homeomorphisms and composition operators on homogeneous Lie groups

Alexander Ukhlov

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arXiv · 2504.11030

Sobolev homeomorphisms and composition operators on homogeneous Lie groups

Alexander Ukhlov

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Abstract

In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism $\varphi: \Omega \to\widetilde{\Omega}$ belongs to the Sobolev space $L^{1}_{q}(\Omega; \widetilde{\Omega})$, $1\leq q < \infty$, if and only if $\varphi$ generates a bounded composition operator on Sobolev spaces.

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Alexander Ukhlov. 2025-04-15. Sobolev homeomorphisms and composition operators on homogeneous Lie groups. https://arxiv.org/abs/2504.11030

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