Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup
Autor(a) principal: | |
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Data de Publicação: | 2010 |
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/10400.1/11664 |
Resumo: | Under the standard assumptions on the variable exponent p(x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space B(alpha)[L(p(-))(R(n))] in terms of the rate of convergence of the Poisson semigroup P(t). We show that the existence of the Riesz fractional derivative D(alpha) f in the space L(p(-))(R(n)) is equivalent to the existence of the limit 1/epsilon(alpha)(I - P(epsilon))(alpha) f. In the pre-limiting case sup(x) p(x) < n/alpha we show that the Bessel potential space is characterized by the condition parallel to(I - P(epsilon))(alpha) f parallel to p((.)) <= C epsilon(alpha). (C) 2009 Elsevier Inc. All rights reserved. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Characterization of the variable exponent Bessel potential spaces via the Poisson semigroupL-P SpacesMaximal-FunctionLebesgue SpacesOperatorsUnder the standard assumptions on the variable exponent p(x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space B(alpha)[L(p(-))(R(n))] in terms of the rate of convergence of the Poisson semigroup P(t). We show that the existence of the Riesz fractional derivative D(alpha) f in the space L(p(-))(R(n)) is equivalent to the existence of the limit 1/epsilon(alpha)(I - P(epsilon))(alpha) f. In the pre-limiting case sup(x) p(x) < n/alpha we show that the Bessel potential space is characterized by the condition parallel to(I - P(epsilon))(alpha) f parallel to p((.)) <= C epsilon(alpha). (C) 2009 Elsevier Inc. All rights reserved.Fundacao para a Ciencia e a Tecnologia (FCT) [SFRFi/BD/22977/2005]Academic Press Inc Elsevier ScienceSapientiaRafeiro, HumbertoSamko, Stefan2018-12-07T14:53:44Z2010-032010-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/11664eng0022-247X10.1016/j.jmaa.2009.11.008info: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:RCAAP2023-07-24T10:23:30Zoai:sapientia.ualg.pt:10400.1/11664Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:03:08.351785Repositório 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 |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
title |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
spellingShingle |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup Rafeiro, Humberto L-P Spaces Maximal-Function Lebesgue Spaces Operators |
title_short |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
title_full |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
title_fullStr |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
title_full_unstemmed |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
title_sort |
Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup |
author |
Rafeiro, Humberto |
author_facet |
Rafeiro, Humberto Samko, Stefan |
author_role |
author |
author2 |
Samko, Stefan |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Rafeiro, Humberto Samko, Stefan |
dc.subject.por.fl_str_mv |
L-P Spaces Maximal-Function Lebesgue Spaces Operators |
topic |
L-P Spaces Maximal-Function Lebesgue Spaces Operators |
description |
Under the standard assumptions on the variable exponent p(x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space B(alpha)[L(p(-))(R(n))] in terms of the rate of convergence of the Poisson semigroup P(t). We show that the existence of the Riesz fractional derivative D(alpha) f in the space L(p(-))(R(n)) is equivalent to the existence of the limit 1/epsilon(alpha)(I - P(epsilon))(alpha) f. In the pre-limiting case sup(x) p(x) < n/alpha we show that the Bessel potential space is characterized by the condition parallel to(I - P(epsilon))(alpha) f parallel to p((.)) <= C epsilon(alpha). (C) 2009 Elsevier Inc. All rights reserved. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-03 2010-03-01T00:00:00Z 2018-12-07T14:53:44Z |
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/10400.1/11664 |
url |
http://hdl.handle.net/10400.1/11664 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0022-247X 10.1016/j.jmaa.2009.11.008 |
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 |
Academic Press Inc Elsevier Science |
publisher.none.fl_str_mv |
Academic Press Inc Elsevier Science |
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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1799133265343283200 |