Local grand Lebesgue spaces on quasi-metric measure spaces and some applications

Detalhes bibliográficos
Autor(a) principal: Rafeiro, Humberto
Data de Publicação: 2022
Outros Autores: Samko, Stefan, Umarkhadzhiev, Salaudin
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/18479
Resumo: We introduce local grand Lebesgue spaces, over a quasi-metric measure space (X, d, mu), where the Lebesgue space is "aggrandized" not everywhere but only at a given closed set F of measure zero. We show that such spaces coincide for different choices of aggrandizers if their Matuszewska-Orlicz indices are positive. Within the framework of such local grand Lebesgue spaces, we study the maximal operator, singular operators with standard kernel, and potential type operators. Finally, we give an application to Dirichlet problem for the Poisson equation, taking F as the boundary of the domain.
id RCAP_113b77fc8d81db3c9f1529eb2cafc516
oai_identifier_str oai:sapientia.ualg.pt:10400.1/18479
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Local grand Lebesgue spaces on quasi-metric measure spaces and some applicationsGrand Lebesgue spacesMaximal functionSingular integralsRiesz potentialWe introduce local grand Lebesgue spaces, over a quasi-metric measure space (X, d, mu), where the Lebesgue space is "aggrandized" not everywhere but only at a given closed set F of measure zero. We show that such spaces coincide for different choices of aggrandizers if their Matuszewska-Orlicz indices are positive. Within the framework of such local grand Lebesgue spaces, we study the maximal operator, singular operators with standard kernel, and potential type operators. Finally, we give an application to Dirichlet problem for the Poisson equation, taking F as the boundary of the domain.SpringerSapientiaRafeiro, HumbertoSamko, StefanUmarkhadzhiev, Salaudin2022-11-09T09:31:31Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/18479eng1385-129210.1007/s11117-022-00915-zinfo: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:RCAAP2023-07-24T10:30:43Zoai:sapientia.ualg.pt:10400.1/18479Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:08:14.346087Repositório 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 Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
spellingShingle Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
Rafeiro, Humberto
Grand Lebesgue spaces
Maximal function
Singular integrals
Riesz potential
title_short Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_full Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_fullStr Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_full_unstemmed Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
title_sort Local grand Lebesgue spaces on quasi-metric measure spaces and some applications
author Rafeiro, Humberto
author_facet Rafeiro, Humberto
Samko, Stefan
Umarkhadzhiev, Salaudin
author_role author
author2 Samko, Stefan
Umarkhadzhiev, Salaudin
author2_role author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Rafeiro, Humberto
Samko, Stefan
Umarkhadzhiev, Salaudin
dc.subject.por.fl_str_mv Grand Lebesgue spaces
Maximal function
Singular integrals
Riesz potential
topic Grand Lebesgue spaces
Maximal function
Singular integrals
Riesz potential
description We introduce local grand Lebesgue spaces, over a quasi-metric measure space (X, d, mu), where the Lebesgue space is "aggrandized" not everywhere but only at a given closed set F of measure zero. We show that such spaces coincide for different choices of aggrandizers if their Matuszewska-Orlicz indices are positive. Within the framework of such local grand Lebesgue spaces, we study the maximal operator, singular operators with standard kernel, and potential type operators. Finally, we give an application to Dirichlet problem for the Poisson equation, taking F as the boundary of the domain.
publishDate 2022
dc.date.none.fl_str_mv 2022-11-09T09:31:31Z
2022
2022-01-01T00:00:00Z
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/10400.1/18479
url http://hdl.handle.net/10400.1/18479
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1385-1292
10.1007/s11117-022-00915-z
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_ 1799133328330194944

Registros relacionados