Refined geometric characterizations of weak p-quasiconformal mappings

Ruslan Salimov; Alexander Ukhlov

doi:10.1007/s41478-024-00855-9

Refined geometric characterizations of weak p-quasiconformal mappings

Ruslan Salimov, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

In this paper, we consider refined geometric characterizations of weak p-quasiconformal mappings φ:Ω→Ω~, where Ω and Ω~ are domains in Rn. We prove that mappings with bounded geometric p-dilatation on the set Ω\S, where S is a set with σ-finite (n-1)-measure, are Sobolev Wp,loc1-mappings and generate bounded composition operators on Sobolev spaces.

Original language	American English
Article number	127826
Pages (from-to)	691-705
Number of pages	15
Journal	Journal of Analysis
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s41478-024-00855-9
State	Published - 1 Apr 2025

Keywords

Composition operators
Quasiconformal mappings
Sobolev spaces

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

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10.1007/s41478-024-00855-9

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N2 - In this paper, we consider refined geometric characterizations of weak p-quasiconformal mappings φ:Ω→Ω~, where Ω and Ω~ are domains in Rn. We prove that mappings with bounded geometric p-dilatation on the set Ω\S, where S is a set with σ-finite (n-1)-measure, are Sobolev Wp,loc1-mappings and generate bounded composition operators on Sobolev spaces.

AB - In this paper, we consider refined geometric characterizations of weak p-quasiconformal mappings φ:Ω→Ω~, where Ω and Ω~ are domains in Rn. We prove that mappings with bounded geometric p-dilatation on the set Ω\S, where S is a set with σ-finite (n-1)-measure, are Sobolev Wp,loc1-mappings and generate bounded composition operators on Sobolev spaces.

KW - Composition operators

KW - Quasiconformal mappings

KW - Sobolev spaces

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M1 - 127826

ER -

Refined geometric characterizations of weak p-quasiconformal mappings

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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