Sharp bounds for composition with quasiconformal mappings in Sobolev spaces

Let φ be a quasiconformal mapping, and let Tφ be the composition operator which maps f to f ˝ φ. Since φ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of Tφ on Lp and W1,p for 1 ă p ă 8. This cases are well understood...

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Autores: Oliva, Marcos, Prats, Martí|||0000-0001-8799-6995
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:287737
Acesso em linha:https://ddd.uab.cat/record/287737
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2017.02.016
Access Level:acceso abierto
Palavra-chave:Sobolev spaces
Fractional smoothness
Quasiconformal mappings
Composition operator
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spelling Sharp bounds for composition with quasiconformal mappings in Sobolev spacesOliva, MarcosPrats, Martí|||0000-0001-8799-6995Sobolev spacesFractional smoothnessQuasiconformal mappingsComposition operatorLet φ be a quasiconformal mapping, and let Tφ be the composition operator which maps f to f ˝ φ. Since φ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of Tφ on Lp and W1,p for 1 ă p ă 8. This cases are well understood but alternative proofs of some known results are provided. Using interpolation techniques it is seen that compactly supported Bessel potential functions in Hs,p are sent to Hs,q whenever 0 ă s ă 1 for appropriate values of q. The techniques used lead to sharp results and they can be applied to Besov spaces as well. 22017-01-0120172017-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/287737https://dx.doi.org/urn:doi:10.1016/j.jmaa.2017.02.016reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengEuropean Commission https://doi.org/10.13039/501100000780 307179Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 SEV-2015-0554Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2011-28198Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-75open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2877372026-06-06T12:50:31Z
dc.title.none.fl_str_mv Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
title Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
spellingShingle Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
Oliva, Marcos
Sobolev spaces
Fractional smoothness
Quasiconformal mappings
Composition operator
title_short Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
title_full Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
title_fullStr Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
title_full_unstemmed Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
title_sort Sharp bounds for composition with quasiconformal mappings in Sobolev spaces
dc.creator.none.fl_str_mv Oliva, Marcos
Prats, Martí|||0000-0001-8799-6995
author Oliva, Marcos
author_facet Oliva, Marcos
Prats, Martí|||0000-0001-8799-6995
author_role author
author2 Prats, Martí|||0000-0001-8799-6995
author2_role author
dc.subject.none.fl_str_mv Sobolev spaces
Fractional smoothness
Quasiconformal mappings
Composition operator
topic Sobolev spaces
Fractional smoothness
Quasiconformal mappings
Composition operator
description Let φ be a quasiconformal mapping, and let Tφ be the composition operator which maps f to f ˝ φ. Since φ may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of Tφ on Lp and W1,p for 1 ă p ă 8. This cases are well understood but alternative proofs of some known results are provided. Using interpolation techniques it is seen that compactly supported Bessel potential functions in Hs,p are sent to Hs,q whenever 0 ă s ă 1 for appropriate values of q. The techniques used lead to sharp results and they can be applied to Besov spaces as well.
publishDate 2017
dc.date.none.fl_str_mv 2
2017-01-01
2017
2017-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/287737
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2017.02.016
url https://ddd.uab.cat/record/287737
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2017.02.016
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission https://doi.org/10.13039/501100000780 307179
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 SEV-2015-0554
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2011-28198
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-75
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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