Sobolev homeomorphisms and composition operators on homogeneous Lie groups

2025/04/15 by Alexander Ukhlov, Ukhlov, Alexander · 1 citation
Mathematics · #22E30 #46E35 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2504.11030

openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism φ: Ω→\widetildeΩ belongs to the Sobolev space L¹_q(Ω; \widetildeΩ), 1≤ q < ∞, if and only if φ generates a bounded composition operator on Sobolev spaces.

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