Composition operators in weighted Sobolev spaces on Carnot groups

Alexander Ukhlov

doi:https://doi.org/10.1007/s10474-011-0104-4

Composition operators in weighted Sobolev spaces on Carnot groups

Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

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

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	American 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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1007/s10474-011-0104-4

Cite this

@article{29ee0275741d4589a9090087caeeec9f,

title = "Composition operators in weighted Sobolev spaces on Carnot groups",

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.",

year = "2011",

month = oct,

day = "1",

doi = "https://doi.org/10.1007/s10474-011-0104-4",

language = "American English",

volume = "133",

pages = "103--127",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Composition operators in weighted Sobolev spaces on Carnot groups

AU - Ukhlov, Alexander

N1 - 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.

PY - 2011/10/1

Y1 - 2011/10/1

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

UR - http://www.scopus.com/inward/record.url?scp=80052292570&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s10474-011-0104-4

DO - https://doi.org/10.1007/s10474-011-0104-4

M3 - Article

SN - 0236-5294

VL - 133

SP - 103

EP - 127

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -

Composition operators in weighted Sobolev spaces on Carnot groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this