COMPOSITION OPERATORS ON SOBOLEV SPACES AND WEIGHTED MODULI INEQUALITIES

Vladimir Gol'dshtein; Evgeny Sevost'yanov; Alexander Ukhlov

doi:10.59277/mrar.2024.26.76.2.101

COMPOSITION OPERATORS ON SOBOLEV SPACES AND WEIGHTED MODULI INEQUALITIES

Vladimir Gol'dshtein, Evgeny Sevost'yanov, Alexander Ukhlov

Department of Mathematics

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

1 Scopus citations

Abstract

In this paper, we study connections between composition operators on Sobolev spaces and mappings defined by p-moduli inequalities (p-capacity inequalities). We prove that weighted moduli inequalities lead to composition operators on corresponding Sobolev spaces and conversely, that composition operators on Sobolev spaces imply weighted moduli inequalities.

Original language	English
Pages (from-to)	101-113
Number of pages	13
Journal	Mathematical Reports
Volume	26-76
Issue number	2
DOIs	https://doi.org/10.59277/mrar.2024.26.76.2.101
State	Published - 1 Jan 2024

Keywords

quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

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10.59277/mrar.2024.26.76.2.101

Cite this

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COMPOSITION OPERATORS ON SOBOLEV SPACES AND WEIGHTED MODULI INEQUALITIES

Abstract

Keywords

ASJC Scopus subject areas

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