Composition operators on Sobolev spaces, Q-mappings and weighted Sobolev inequalities

Alexander Menovschikov; Alexander Ukhlov

doi:10.48550/arXiv.2110.09261

Composition operators on Sobolev spaces, Q-mappings and weighted Sobolev inequalities

Alexander Menovschikov, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Working paper › Preprint

Abstract

In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and Q-mappings. On this base we obtain measure distortion properties Q-homeomorphisms. Using the composition operators on Sobolev spaces we obtain weighted Sobolev inequalities with special weights which are Jacobians of Q-mappings.

Original language	American English
DOIs	https://doi.org/10.48550/arXiv.2110.09261
State	Published - 18 Oct 2021

Keywords

46E35, 30C65
math.AP

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10.48550/arXiv.2110.09261

Cite this

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abstract = "In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and Q-mappings. On this base we obtain measure distortion properties Q-homeomorphisms. Using the composition operators on Sobolev spaces we obtain weighted Sobolev inequalities with special weights which are Jacobians of Q-mappings.",

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AB - In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and Q-mappings. On this base we obtain measure distortion properties Q-homeomorphisms. Using the composition operators on Sobolev spaces we obtain weighted Sobolev inequalities with special weights which are Jacobians of Q-mappings.

KW - 46E35, 30C65

KW - math.AP

U2 - 10.48550/arXiv.2110.09261

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M3 - Preprint

BT - Composition operators on Sobolev spaces, Q-mappings and weighted Sobolev inequalities

ER -

Composition operators on Sobolev spaces, Q-mappings and weighted Sobolev inequalities

Abstract

Keywords

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Cite this