Composition operators in weighted Sobolev spaces on Carnot groups

Alexander Ukhlov

doi:10.1007/s10474-011-0104-4

Composition operators in weighted Sobolev spaces on Carnot groups

Alexander Ukhlov

Department of Mathematics

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

3 Scopus citations

Abstract

We study mappings that generate bounded composition operators in weighted Sobolev spaces on Carnot groups. A complete analytical description of these mappings is given in terms of integrability of distortion of mappings in weighted Lebesgue spaces. We define weighted Sobolev mappings and study their connection with ACL-mappings. As an application we obtain weighted Sobolev type embedding theorems on Carnot groups.

Original language	English
Pages (from-to)	103-127
Number of pages	25
Journal	Acta Mathematica Hungarica
Volume	133
Issue number	1
DOIs	https://doi.org/10.1007/s10474-011-0104-4
State	Published - 1 Oct 2011

Keywords

Carnot group
composition operator
weighted Sobolev space

ASJC Scopus subject areas

Mathematics (all)

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10.1007/s10474-011-0104-4

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abstract = "We study mappings that generate bounded composition operators in weighted Sobolev spaces on Carnot groups. A complete analytical description of these mappings is given in terms of integrability of distortion of mappings in weighted Lebesgue spaces. We define weighted Sobolev mappings and study their connection with ACL-mappings. As an application we obtain weighted Sobolev type embedding theorems on Carnot groups.",

keywords = "Carnot group, composition operator, weighted Sobolev space",

author = "Alexander Ukhlov",

note = "Funding Information: ∗This work was partially supported by ISF grant No 1033/07. Key words and phrases: weighted Sobolev space, composition operator, Carnot group. 2000 Mathematics Subject Classification: 46E35, 58J05.",

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N2 - We study mappings that generate bounded composition operators in weighted Sobolev spaces on Carnot groups. A complete analytical description of these mappings is given in terms of integrability of distortion of mappings in weighted Lebesgue spaces. We define weighted Sobolev mappings and study their connection with ACL-mappings. As an application we obtain weighted Sobolev type embedding theorems on Carnot groups.

AB - We study mappings that generate bounded composition operators in weighted Sobolev spaces on Carnot groups. A complete analytical description of these mappings is given in terms of integrability of distortion of mappings in weighted Lebesgue spaces. We define weighted Sobolev mappings and study their connection with ACL-mappings. As an application we obtain weighted Sobolev type embedding theorems on Carnot groups.

KW - Carnot group

KW - composition operator

KW - weighted Sobolev space

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JO - Acta Mathematica Hungarica

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ER -

Composition operators in weighted Sobolev spaces on Carnot groups

Abstract

Keywords

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