On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators

Detalhes bibliográficos
Autor(a) principal: Alabalik, Aysegul Ç.
Data de Publicação: 2019
Outros Autores: Almeida, Alexandre, Samko, Stefan
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/27193
Resumo: We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of C∞0(Rn) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy–Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.
id RCAP_b1f59c23eac33f51f86b35f997448185
oai_identifier_str oai:ria.ua.pt:10773/27193
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operatorsMorrey spacesVanishing propertiesMaximal functionsPotential operatorsSingular operatorsHardy operatorsWe consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of C∞0(Rn) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy–Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.Springer2019-12-16T17:03:31Z2021-07-31T00:00:00Z2020-07-01T00:00:00Z2020-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/27193eng1735-878710.1007/s43037-019-00049-7Alabalik, Aysegul Ç.Almeida, AlexandreSamko, Stefaninfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:52:26Zoai:ria.ua.pt:10773/27193Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:56.321804Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
title On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
spellingShingle On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
Alabalik, Aysegul Ç.
Morrey spaces
Vanishing properties
Maximal functions
Potential operators
Singular operators
Hardy operators
title_short On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
title_full On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
title_fullStr On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
title_full_unstemmed On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
title_sort On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
author Alabalik, Aysegul Ç.
author_facet Alabalik, Aysegul Ç.
Almeida, Alexandre
Samko, Stefan
author_role author
author2 Almeida, Alexandre
Samko, Stefan
author2_role author
author
dc.contributor.author.fl_str_mv Alabalik, Aysegul Ç.
Almeida, Alexandre
Samko, Stefan
dc.subject.por.fl_str_mv Morrey spaces
Vanishing properties
Maximal functions
Potential operators
Singular operators
Hardy operators
topic Morrey spaces
Vanishing properties
Maximal functions
Potential operators
Singular operators
Hardy operators
description We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of C∞0(Rn) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy–Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.
publishDate 2019
dc.date.none.fl_str_mv 2019-12-16T17:03:31Z
2020-07-01T00:00:00Z
2020-07
2021-07-31T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/27193
url http://hdl.handle.net/10773/27193
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1735-8787
10.1007/s43037-019-00049-7
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799137654229434368

Registros relacionados