Weighted Sobolev theorem in Lebesgue spaces with variable exponent

Detalhes bibliográficos
Autor(a) principal: Samko, N. G.
Data de Publicação: 2007
Outros Autores: Samko, Stefan, Vakulov, B. G.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: http://hdl.handle.net/10400.1/11813
Resumo: For the Riesz potential operator I-alpha there are proved weighted estimates [GRAPHICS] within the framework of weighted Lebesgue spaces L (P(center dot)) (Omega, omega) with variable exponent. In case Omega is a bounded domain, the order alpha = alpha (x) is allowed to be variable as well. The weight functions are radial type functions "fixed" to a finite point and/or to infinity and have a typical feature of Muckenhoupt-Wheeden weights: they may oscillate between two power functions. Conditions on weights are given in terms of their Boyd-type indices. An analogue of such a weighted estimate is also obtained for spherical potential operators on the unit sphere S-n subset of R-n. (c) 2007 Elsevier Inc. All rights reserved.
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spelling Weighted Sobolev theorem in Lebesgue spaces with variable exponentSpherical potential-operatorsFractional integralsMaximal-functionConvolutionFor the Riesz potential operator I-alpha there are proved weighted estimates [GRAPHICS] within the framework of weighted Lebesgue spaces L (P(center dot)) (Omega, omega) with variable exponent. In case Omega is a bounded domain, the order alpha = alpha (x) is allowed to be variable as well. The weight functions are radial type functions "fixed" to a finite point and/or to infinity and have a typical feature of Muckenhoupt-Wheeden weights: they may oscillate between two power functions. Conditions on weights are given in terms of their Boyd-type indices. An analogue of such a weighted estimate is also obtained for spherical potential operators on the unit sphere S-n subset of R-n. (c) 2007 Elsevier Inc. All rights reserved.ElsevierSapientiaSamko, N. G.Samko, StefanVakulov, B. G.2018-12-07T14:58:01Z2007-112007-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/11813eng0022-247X1096-081310.1016/j.jmaa.2007.01.091info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-18T17:32:13Zoai:sapientia.ualg.pt:10400.1/11813Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T20:25:47.281850Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Weighted Sobolev theorem in Lebesgue spaces with variable exponent
title Weighted Sobolev theorem in Lebesgue spaces with variable exponent
spellingShingle Weighted Sobolev theorem in Lebesgue spaces with variable exponent
Samko, N. G.
Spherical potential-operators
Fractional integrals
Maximal-function
Convolution
title_short Weighted Sobolev theorem in Lebesgue spaces with variable exponent
title_full Weighted Sobolev theorem in Lebesgue spaces with variable exponent
title_fullStr Weighted Sobolev theorem in Lebesgue spaces with variable exponent
title_full_unstemmed Weighted Sobolev theorem in Lebesgue spaces with variable exponent
title_sort Weighted Sobolev theorem in Lebesgue spaces with variable exponent
author Samko, N. G.
author_facet Samko, N. G.
Samko, Stefan
Vakulov, B. G.
author_role author
author2 Samko, Stefan
Vakulov, B. G.
author2_role author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Samko, N. G.
Samko, Stefan
Vakulov, B. G.
dc.subject.por.fl_str_mv Spherical potential-operators
Fractional integrals
Maximal-function
Convolution
topic Spherical potential-operators
Fractional integrals
Maximal-function
Convolution
description For the Riesz potential operator I-alpha there are proved weighted estimates [GRAPHICS] within the framework of weighted Lebesgue spaces L (P(center dot)) (Omega, omega) with variable exponent. In case Omega is a bounded domain, the order alpha = alpha (x) is allowed to be variable as well. The weight functions are radial type functions "fixed" to a finite point and/or to infinity and have a typical feature of Muckenhoupt-Wheeden weights: they may oscillate between two power functions. Conditions on weights are given in terms of their Boyd-type indices. An analogue of such a weighted estimate is also obtained for spherical potential operators on the unit sphere S-n subset of R-n. (c) 2007 Elsevier Inc. All rights reserved.
publishDate 2007
dc.date.none.fl_str_mv 2007-11
2007-11-01T00:00:00Z
2018-12-07T14:58:01Z
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/10400.1/11813
url http://hdl.handle.net/10400.1/11813
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-247X
1096-0813
10.1016/j.jmaa.2007.01.091
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 Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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