On mappings generating embedding operators in Sobolev classes on metric measure spaces

Alexander Menovschikov; Alexander Ukhlov

doi:10.1016/j.jmaa.2025.129716

On mappings generating embedding operators in Sobolev classes on metric measure spaces

Alexander Menovschikov
, Alexander Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this article, we study homeomorphisms φ:Ω→Ω˜ that generate embedding operators in Sobolev classes on metric measure spaces X by the composition rule φ^⁎(f)=f∘φ. In turn, this leads to Sobolev type embedding theorems for a wide class of domains Ω˜⊂X.

Original language	English
Article number	129716
Journal	Journal of Mathematical Analysis and Applications
Volume	551
Issue number	2P2
DOIs	https://doi.org/10.1016/j.jmaa.2025.129716
State	Published - 15 Nov 2025

Keywords

Composition operators
Metric measure spaces
Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2025.129716

Cite this

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title = "On mappings generating embedding operators in Sobolev classes on metric measure spaces",

abstract = "In this article, we study homeomorphisms φ:Ω→Ω˜ that generate embedding operators in Sobolev classes on metric measure spaces X by the composition rule φ⁎(f)=f∘φ. In turn, this leads to Sobolev type embedding theorems for a wide class of domains Ω˜⊂X.",

keywords = "Composition operators, Metric measure spaces, Sobolev spaces",

author = "Alexander Menovschikov and Alexander Ukhlov",

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doi = "10.1016/j.jmaa.2025.129716",

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AU - Menovschikov, Alexander

AU - Ukhlov, Alexander

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N2 - In this article, we study homeomorphisms φ:Ω→Ω˜ that generate embedding operators in Sobolev classes on metric measure spaces X by the composition rule φ⁎(f)=f∘φ. In turn, this leads to Sobolev type embedding theorems for a wide class of domains Ω˜⊂X.

AB - In this article, we study homeomorphisms φ:Ω→Ω˜ that generate embedding operators in Sobolev classes on metric measure spaces X by the composition rule φ⁎(f)=f∘φ. In turn, this leads to Sobolev type embedding theorems for a wide class of domains Ω˜⊂X.

KW - Composition operators

KW - Metric measure spaces

KW - Sobolev spaces

UR - https://www.scopus.com/pages/publications/105006665535

U2 - 10.1016/j.jmaa.2025.129716

DO - 10.1016/j.jmaa.2025.129716

M3 - Article

AN - SCOPUS:105006665535

SN - 0022-247X

VL - 551

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2P2

M1 - 129716

ER -

On mappings generating embedding operators in Sobolev classes on metric measure spaces

Abstract

Keywords

ASJC Scopus subject areas

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