Hardy type inequalityin variable lebesgue spaces

Bibliographic Details
Main Author: Rafeiro, Humberto
Publication Date: 2009
Other Authors: Samko, Stefan
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.1/12094
Summary: We prove that in variable exponent spaces where L-p(.)(Omega), where p(.) satisfies the log-condition and Omega is a bounded domain in R-n with the property that R-n\(Omega) over bar has the cone property, the validity of the Hardy type inequality parallel to 1/delta(x)(alpha)integral(Omega)phi(y)/vertical bar x-y vertical bar(n-alpha)dy parallel to(p(.)) <= C parallel to phi parallel to(p(.)), 0 < alpha < min (1, n/p(+)), where delta(x) is approximately equal to dist(x, partial derivative Omega), is equivalent to a certain property of the domain Omega expressed in terms of alpha and chi(Omega).
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spelling Hardy type inequalityin variable lebesgue spacesGeneralized LebesgueMaximal-FunctionSobolev SpacesL-P(Center-Dot)OperatorsWe prove that in variable exponent spaces where L-p(.)(Omega), where p(.) satisfies the log-condition and Omega is a bounded domain in R-n with the property that R-n\(Omega) over bar has the cone property, the validity of the Hardy type inequality parallel to 1/delta(x)(alpha)integral(Omega)phi(y)/vertical bar x-y vertical bar(n-alpha)dy parallel to(p(.)) <= C parallel to phi parallel to(p(.)), 0 < alpha < min (1, n/p(+)), where delta(x) is approximately equal to dist(x, partial derivative Omega), is equivalent to a certain property of the domain Omega expressed in terms of alpha and chi(Omega).Suomalainen TiedeakatemiaSapientiaRafeiro, HumbertoSamko, Stefan2018-12-07T14:58:34Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/12094eng1239-629Xinfo: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:RCAAP2025-02-18T17:40:59Zoai:sapientia.ualg.pt:10400.1/12094Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T20:31:43.393701Repositórios 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 Hardy type inequalityin variable lebesgue spaces
title Hardy type inequalityin variable lebesgue spaces
spellingShingle Hardy type inequalityin variable lebesgue spaces
Rafeiro, Humberto
Generalized Lebesgue
Maximal-Function
Sobolev Spaces
L-P(Center-Dot)
Operators
title_short Hardy type inequalityin variable lebesgue spaces
title_full Hardy type inequalityin variable lebesgue spaces
title_fullStr Hardy type inequalityin variable lebesgue spaces
title_full_unstemmed Hardy type inequalityin variable lebesgue spaces
title_sort Hardy type inequalityin variable lebesgue spaces
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 Generalized Lebesgue
Maximal-Function
Sobolev Spaces
L-P(Center-Dot)
Operators
topic Generalized Lebesgue
Maximal-Function
Sobolev Spaces
L-P(Center-Dot)
Operators
description We prove that in variable exponent spaces where L-p(.)(Omega), where p(.) satisfies the log-condition and Omega is a bounded domain in R-n with the property that R-n\(Omega) over bar has the cone property, the validity of the Hardy type inequality parallel to 1/delta(x)(alpha)integral(Omega)phi(y)/vertical bar x-y vertical bar(n-alpha)dy parallel to(p(.)) <= C parallel to phi parallel to(p(.)), 0 < alpha < min (1, n/p(+)), where delta(x) is approximately equal to dist(x, partial derivative Omega), is equivalent to a certain property of the domain Omega expressed in terms of alpha and chi(Omega).
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01T00:00:00Z
2018-12-07T14:58:34Z
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/10400.1/12094
url http://hdl.handle.net/10400.1/12094
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1239-629X
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 Suomalainen Tiedeakatemia
publisher.none.fl_str_mv Suomalainen Tiedeakatemia
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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