Refined geometric characterizations of weak p-quasiconformal mappings

Ruslan Salimov; Alexander Ukhlov

doi:https://doi.org/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
Journal	Journal of Analysis
DOIs	https://doi.org/10.1007/s41478-024-00855-9
State	Accepted/In press - 1 Jan 2024

Keywords

Composition operators
Quasiconformal mappings
Sobolev spaces

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

Access to Document

https://doi.org/10.1007/s41478-024-00855-9

Cite this

@article{c150503f31a040049fa893451fc2a3e1,

title = "Refined geometric characterizations of weak p-quasiconformal mappings",

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.",

keywords = "Composition operators, Quasiconformal mappings, Sobolev spaces",

author = "Ruslan Salimov and Alexander Ukhlov",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",

year = "2024",

month = jan,

day = "1",

doi = "https://doi.org/10.1007/s41478-024-00855-9",

language = "American English",

journal = "Journal of Analysis",

issn = "0971-3611",

publisher = "Springer Science and Business Media B.V.",

}

TY - JOUR

T1 - Refined geometric characterizations of weak p-quasiconformal mappings

AU - Salimov, Ruslan

AU - Ukhlov, Alexander

PY - 2024/1/1

Y1 - 2024/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=85212083173&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s41478-024-00855-9

DO - https://doi.org/10.1007/s41478-024-00855-9

M3 - Article

SN - 0971-3611

JO - Journal of Analysis

JF - Journal of Analysis

M1 - 127826

ER -

Refined geometric characterizations of weak p-quasiconformal mappings

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this