Mixed norm Bergman-Morrey-type spaces on the unit disc
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10400.1/9403 |
Resumo: | We introduce and study the mixed-norm Bergman-Morrey space A (q;p,lambda) , mixednorm Bergman-Morrey space of local type A (loc) (q;p,lambda) , and mixed-norm Bergman-Morrey space of complementary type (C) A (q;p,lambda) on the unit disk D in the complex plane C. Themixed norm Lebesgue-Morrey space L (q;p,lambda) is defined by the requirement that the sequence of Morrey L (p,lambda)(I)-norms of the Fourier coefficients of a function f belongs to l (q) (I = (0, 1)). Then, A (q;p,lambda) is defined as the subspace of analytic functions in L (q;p,lambda) . Two other spaces A q;p,lambda loc and (C) A (q;p,lambda) are defined similarly by using the local Morrey L (loc) (p,lambda) (I)-norm and the complementary Morrey (C) L (p,lambda)(I)-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman-Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces. |
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Mixed norm Bergman-Morrey-type spaces on the unit discBergman–Morrey-type spaceMixed normWe introduce and study the mixed-norm Bergman-Morrey space A (q;p,lambda) , mixednorm Bergman-Morrey space of local type A (loc) (q;p,lambda) , and mixed-norm Bergman-Morrey space of complementary type (C) A (q;p,lambda) on the unit disk D in the complex plane C. Themixed norm Lebesgue-Morrey space L (q;p,lambda) is defined by the requirement that the sequence of Morrey L (p,lambda)(I)-norms of the Fourier coefficients of a function f belongs to l (q) (I = (0, 1)). Then, A (q;p,lambda) is defined as the subspace of analytic functions in L (q;p,lambda) . Two other spaces A q;p,lambda loc and (C) A (q;p,lambda) are defined similarly by using the local Morrey L (loc) (p,lambda) (I)-norm and the complementary Morrey (C) L (p,lambda)(I)-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman-Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces.MAIK Nauka/InterperiodicaSapientiaSamko, StefanKarapetyants, A. N.2017-04-07T15:56:24Z2016-072016-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/9403eng0001-434610.1134/S000143461607004Xinfo: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:RCAAP2023-07-24T10:20:51Zoai:sapientia.ualg.pt:10400.1/9403Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:01:21.572860Repositório 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 |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
title |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
spellingShingle |
Mixed norm Bergman-Morrey-type spaces on the unit disc Samko, Stefan Bergman–Morrey-type space Mixed norm |
title_short |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
title_full |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
title_fullStr |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
title_full_unstemmed |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
title_sort |
Mixed norm Bergman-Morrey-type spaces on the unit disc |
author |
Samko, Stefan |
author_facet |
Samko, Stefan Karapetyants, A. N. |
author_role |
author |
author2 |
Karapetyants, A. N. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Samko, Stefan Karapetyants, A. N. |
dc.subject.por.fl_str_mv |
Bergman–Morrey-type space Mixed norm |
topic |
Bergman–Morrey-type space Mixed norm |
description |
We introduce and study the mixed-norm Bergman-Morrey space A (q;p,lambda) , mixednorm Bergman-Morrey space of local type A (loc) (q;p,lambda) , and mixed-norm Bergman-Morrey space of complementary type (C) A (q;p,lambda) on the unit disk D in the complex plane C. Themixed norm Lebesgue-Morrey space L (q;p,lambda) is defined by the requirement that the sequence of Morrey L (p,lambda)(I)-norms of the Fourier coefficients of a function f belongs to l (q) (I = (0, 1)). Then, A (q;p,lambda) is defined as the subspace of analytic functions in L (q;p,lambda) . Two other spaces A q;p,lambda loc and (C) A (q;p,lambda) are defined similarly by using the local Morrey L (loc) (p,lambda) (I)-norm and the complementary Morrey (C) L (p,lambda)(I)-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman-Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-07 2016-07-01T00:00:00Z 2017-04-07T15:56:24Z |
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/10400.1/9403 |
url |
http://hdl.handle.net/10400.1/9403 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0001-4346 10.1134/S000143461607004X |
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 |
MAIK Nauka/Interperiodica |
publisher.none.fl_str_mv |
MAIK Nauka/Interperiodica |
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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1799133242634272768 |