Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces
Autor(a) principal: | |
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Data de Publicação: | 2013 |
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/10400.1/11724 |
Resumo: | We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r). |
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Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spacesSufficient conditionsRiesz-potentialsLebesgue spacesHomogeneous typeBoundednessL-P(Center-Dot)We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).Science Development Foundation under the President of the Republic of Azerbaijan [EIF-2010-1(1)-40/06-1]; Scientific and Technological Research Council of Turkey (TUBITAK) [110T695]Academic Press Inc Elsevier ScienceSapientiaGuliyev, Vagif S.Hasanov, Javanshir J.Samko, Stefan2018-12-07T14:57:50Z2013-052013-05-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/11724eng0022-247X10.1016/j.jmaa.2012.03.041info: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:RCAAP2023-07-24T10:23:34Zoai:sapientia.ualg.pt:10400.1/11724Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:03:11.334510Repositório 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 |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
title |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
spellingShingle |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces Guliyev, Vagif S. Sufficient conditions Riesz-potentials Lebesgue spaces Homogeneous type Boundedness L-P(Center-Dot) |
title_short |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
title_full |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
title_fullStr |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
title_full_unstemmed |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
title_sort |
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces |
author |
Guliyev, Vagif S. |
author_facet |
Guliyev, Vagif S. Hasanov, Javanshir J. Samko, Stefan |
author_role |
author |
author2 |
Hasanov, Javanshir J. Samko, Stefan |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Guliyev, Vagif S. Hasanov, Javanshir J. Samko, Stefan |
dc.subject.por.fl_str_mv |
Sufficient conditions Riesz-potentials Lebesgue spaces Homogeneous type Boundedness L-P(Center-Dot) |
topic |
Sufficient conditions Riesz-potentials Lebesgue spaces Homogeneous type Boundedness L-P(Center-Dot) |
description |
We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r). |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-05 2013-05-01T00:00:00Z 2018-12-07T14:57:50Z |
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/10400.1/11724 |
url |
http://hdl.handle.net/10400.1/11724 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0022-247X 10.1016/j.jmaa.2012.03.041 |
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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1799133266164318208 |