Sobolev homeomorphisms and composition operators on homogeneous Lie groups

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-12-23 DOI:10.1007/s10474-025-01579-3

A. Ukhlov

引用次数: 0

Abstract

In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism \(\varphi \colon \Omega \to\widetilde{\Omega}\) 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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齐次李群上的Sobolev同胚和复合算子

本文研究了齐次李群上的Sobolev同胚和复合算子。证明了一个可测同胚\(\varphi \colon \Omega \to\widetilde{\Omega}\)属于Sobolev空间\(L^{1}_{q}(\Omega; \widetilde{\Omega})\), \(1\leq q < \infty\)，当且仅当\(\varphi\)在Sobolev空间上生成有界复合算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.