A T(1) theorem for fractional Sobolev spaces on domains

Given any uniform domain Ω, the Triebel-Lizorkin space Fsp,qpΩq with 0 ă s ă 1 and 1 ă p, q ă 8 can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(...

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Autores: Prats, Martí|||0000-0001-8799-6995, Saksman, Eero|||0000-0002-7630-7135
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:287736
Acceso en línea:https://ddd.uab.cat/record/287736
https://dx.doi.org/urn:doi:10.1007/s12220-017-9770-y
Access Level:acceso abierto
Palabra clave:Sobolev
Triebel-Lizorkin
Besov
Calderón-Zygmund operators
Fourier multipliers
First-order differences
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spelling A T(1) theorem for fractional Sobolev spaces on domainsPrats, Martí|||0000-0001-8799-6995Saksman, Eero|||0000-0002-7630-7135SobolevTriebel-LizorkinBesovCalderón-Zygmund operatorsFourier multipliersFirst-order differencesGiven any uniform domain Ω, the Triebel-Lizorkin space Fsp,qpΩq with 0 ă s ă 1 and 1 ă p, q ă 8 can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(1)-theorem for fractional Sobolev spaces with 0 ă s ă 1 for any uniform domain and for a large family of Calder'on-Zygmund operators in any ambient space Rd as long as sp ą d. 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/287736https://dx.doi.org/urn:doi:10.1007/s12220-017-9770-yreponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengEuropean Commission https://doi.org/10.13039/501100000780 320501Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-44304-PMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM-2010-16232Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-75Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/FI-B200107open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2877362026-06-06T12:50:31Z
dc.title.none.fl_str_mv A T(1) theorem for fractional Sobolev spaces on domains
title A T(1) theorem for fractional Sobolev spaces on domains
spellingShingle A T(1) theorem for fractional Sobolev spaces on domains
Prats, Martí|||0000-0001-8799-6995
Sobolev
Triebel-Lizorkin
Besov
Calderón-Zygmund operators
Fourier multipliers
First-order differences
title_short A T(1) theorem for fractional Sobolev spaces on domains
title_full A T(1) theorem for fractional Sobolev spaces on domains
title_fullStr A T(1) theorem for fractional Sobolev spaces on domains
title_full_unstemmed A T(1) theorem for fractional Sobolev spaces on domains
title_sort A T(1) theorem for fractional Sobolev spaces on domains
dc.creator.none.fl_str_mv Prats, Martí|||0000-0001-8799-6995
Saksman, Eero|||0000-0002-7630-7135
author Prats, Martí|||0000-0001-8799-6995
author_facet Prats, Martí|||0000-0001-8799-6995
Saksman, Eero|||0000-0002-7630-7135
author_role author
author2 Saksman, Eero|||0000-0002-7630-7135
author2_role author
dc.subject.none.fl_str_mv Sobolev
Triebel-Lizorkin
Besov
Calderón-Zygmund operators
Fourier multipliers
First-order differences
topic Sobolev
Triebel-Lizorkin
Besov
Calderón-Zygmund operators
Fourier multipliers
First-order differences
description Given any uniform domain Ω, the Triebel-Lizorkin space Fsp,qpΩq with 0 ă s ă 1 and 1 ă p, q ă 8 can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(1)-theorem for fractional Sobolev spaces with 0 ă s ă 1 for any uniform domain and for a large family of Calder'on-Zygmund operators in any ambient space Rd as long as sp ą d.
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/287736
https://dx.doi.org/urn:doi:10.1007/s12220-017-9770-y
url https://ddd.uab.cat/record/287736
https://dx.doi.org/urn:doi:10.1007/s12220-017-9770-y
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 320501
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-44304-P
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM-2010-16232
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-75
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/FI-B200107
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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://rightsstatements.org/vocab/InC/1.0/
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
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