Weighted hardy operators in complementary morrey spaces
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/12061 |
Resumo: | We study the weighted p -> q-boundedness of the multidimensional weighted Hardy-type operators H-omega(alpha) and H-omega(alpha) with radial type weight omega = omega(vertical bar x vertical bar), in the generalized complementary Morrey spaces (C) L-(0)(p,psi) (R-n) defined by an almost increasing function psi = psi(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed on psi and omega, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function psi and the weight omega are power functions. We also prove that the spaces (C) L-(0)(p,psi) (Omega) over bounded domains Omega are embedded between weighted Lebesgue space L-p with the weight psi and such a space with the weight psi, perturbed by a logarithmic factor. Both the embeddings are sharp. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Weighted hardy operators in complementary morrey spacesSingular operatorsWe study the weighted p -> q-boundedness of the multidimensional weighted Hardy-type operators H-omega(alpha) and H-omega(alpha) with radial type weight omega = omega(vertical bar x vertical bar), in the generalized complementary Morrey spaces (C) L-(0)(p,psi) (R-n) defined by an almost increasing function psi = psi(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed on psi and omega, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function psi and the weight omega are power functions. We also prove that the spaces (C) L-(0)(p,psi) (Omega) over bounded domains Omega are embedded between weighted Lebesgue space L-p with the weight psi and such a space with the weight psi, perturbed by a logarithmic factor. Both the embeddings are sharp.Lulea University of TechnologyHindawi LtdSapientiaLukkassen, DagPersson, Lars-ErikSamko, Stefan2018-12-07T14:58:30Z20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/12061eng2090-899710.1155/2012/283285info: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:RCAAP2023-07-24T10:23:59Zoai:sapientia.ualg.pt:10400.1/12061Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:03:28.510307Repositório 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 |
Weighted hardy operators in complementary morrey spaces |
title |
Weighted hardy operators in complementary morrey spaces |
spellingShingle |
Weighted hardy operators in complementary morrey spaces Lukkassen, Dag Singular operators |
title_short |
Weighted hardy operators in complementary morrey spaces |
title_full |
Weighted hardy operators in complementary morrey spaces |
title_fullStr |
Weighted hardy operators in complementary morrey spaces |
title_full_unstemmed |
Weighted hardy operators in complementary morrey spaces |
title_sort |
Weighted hardy operators in complementary morrey spaces |
author |
Lukkassen, Dag |
author_facet |
Lukkassen, Dag Persson, Lars-Erik Samko, Stefan |
author_role |
author |
author2 |
Persson, Lars-Erik Samko, Stefan |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Lukkassen, Dag Persson, Lars-Erik Samko, Stefan |
dc.subject.por.fl_str_mv |
Singular operators |
topic |
Singular operators |
description |
We study the weighted p -> q-boundedness of the multidimensional weighted Hardy-type operators H-omega(alpha) and H-omega(alpha) with radial type weight omega = omega(vertical bar x vertical bar), in the generalized complementary Morrey spaces (C) L-(0)(p,psi) (R-n) defined by an almost increasing function psi = psi(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed on psi and omega, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function psi and the weight omega are power functions. We also prove that the spaces (C) L-(0)(p,psi) (Omega) over bounded domains Omega are embedded between weighted Lebesgue space L-p with the weight psi and such a space with the weight psi, perturbed by a logarithmic factor. Both the embeddings are sharp. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2012-01-01T00:00:00Z 2018-12-07T14:58:30Z |
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/10400.1/12061 |
url |
http://hdl.handle.net/10400.1/12061 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2090-8997 10.1155/2012/283285 |
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 |
Hindawi Ltd |
publisher.none.fl_str_mv |
Hindawi Ltd |
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 |
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1799133268945141760 |