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

Detalhes bibliográficos
Autor(a) principal: Alabalik, Aysegul C.
Data de Publicação: 2020
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/10400.1/16600
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(infinity) (R-n) 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.
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spelling On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operatorsMorrey spacesVanishing propertiesMaximal functionsPotential operatorsSingular operatorsHardy operatorsMathematicsWe 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(infinity) (R-n) 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.CIDMA (Center for Research and Development in Mathematics and Applications)FCT (Portuguese Foundation for Science and Technology)Portuguese Foundation for Science and Technology [UID/MAT/04106/2019]Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-01-00223, 18-01-00094-a]SpringerSapientiaAlabalik, Aysegul C.Almeida, AlexandreSamko, Stefan2021-06-24T11:36:00Z2020-072020-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/16600eng2662-203310.1007/s43037-019-00049-7info: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:RCAAP2023-07-24T10:28:34Zoai:sapientia.ualg.pt:10400.1/16600Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:06:42.769445Repositório 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 C.
Morrey spaces
Vanishing properties
Maximal functions
Potential operators
Singular operators
Hardy operators
Mathematics
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 C.
author_facet Alabalik, Aysegul C.
Almeida, Alexandre
Samko, Stefan
author_role author
author2 Almeida, Alexandre
Samko, Stefan
author2_role author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Alabalik, Aysegul C.
Almeida, Alexandre
Samko, Stefan
dc.subject.por.fl_str_mv Morrey spaces
Vanishing properties
Maximal functions
Potential operators
Singular operators
Hardy operators
Mathematics
topic Morrey spaces
Vanishing properties
Maximal functions
Potential operators
Singular operators
Hardy operators
Mathematics
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(infinity) (R-n) 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 2020
dc.date.none.fl_str_mv 2020-07
2020-07-01T00:00:00Z
2021-06-24T11:36:00Z
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/10400.1/16600
url http://hdl.handle.net/10400.1/16600
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2662-2033
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
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