Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II
Autor(a) principal: | |
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Data de Publicação: | 2007 |
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/10400.1/11392 |
Resumo: | In [S.G. Samko, B.G. Vakulov, Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, J. Math. Anal. Appl. 310 (2005) 229-246], Sobolev-type p((.)) -> q((.))-theorems were proved for the Riesz potential operator I-alpha in the weighted Lebesgue generalized spaces L-p(.)(R-n, p) with the variable exponent p(x) and a two-parameter power weight fixed to an arbitrary finite point x(0) and to infinity, under an additional condition relating the weight exponents at x(0) and at infinity. We show in this note that those theorems are valid without this additional condition. Similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces L-p(.) (S-n, p) on the unit sphere S-n in Rn+1 are also improved in the same way. (c) 2006 Elsevier Inc. All rights reserved. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, IIIn [S.G. Samko, B.G. Vakulov, Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, J. Math. Anal. Appl. 310 (2005) 229-246], Sobolev-type p((.)) -> q((.))-theorems were proved for the Riesz potential operator I-alpha in the weighted Lebesgue generalized spaces L-p(.)(R-n, p) with the variable exponent p(x) and a two-parameter power weight fixed to an arbitrary finite point x(0) and to infinity, under an additional condition relating the weight exponents at x(0) and at infinity. We show in this note that those theorems are valid without this additional condition. Similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces L-p(.) (S-n, p) on the unit sphere S-n in Rn+1 are also improved in the same way. (c) 2006 Elsevier Inc. All rights reserved.Academic Press Inc Elsevier ScienceSapientiaSamko, S.Shargorodsky, E.Vakulov, B.2018-12-07T14:53:11Z2007-012007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/11392eng0022-247X10.1016/j.jmaa.2006.01.069info: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:RCAAP2023-07-24T10:23:11Zoai:sapientia.ualg.pt:10400.1/11392Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:02:54.601581Repositório 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 |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
title |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
spellingShingle |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II Samko, S. |
title_short |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
title_full |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
title_fullStr |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
title_full_unstemmed |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
title_sort |
Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, II |
author |
Samko, S. |
author_facet |
Samko, S. Shargorodsky, E. Vakulov, B. |
author_role |
author |
author2 |
Shargorodsky, E. Vakulov, B. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Samko, S. Shargorodsky, E. Vakulov, B. |
description |
In [S.G. Samko, B.G. Vakulov, Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, J. Math. Anal. Appl. 310 (2005) 229-246], Sobolev-type p((.)) -> q((.))-theorems were proved for the Riesz potential operator I-alpha in the weighted Lebesgue generalized spaces L-p(.)(R-n, p) with the variable exponent p(x) and a two-parameter power weight fixed to an arbitrary finite point x(0) and to infinity, under an additional condition relating the weight exponents at x(0) and at infinity. We show in this note that those theorems are valid without this additional condition. Similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces L-p(.) (S-n, p) on the unit sphere S-n in Rn+1 are also improved in the same way. (c) 2006 Elsevier Inc. All rights reserved. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-01 2007-01-01T00:00:00Z 2018-12-07T14:53:11Z |
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/10400.1/11392 |
url |
http://hdl.handle.net/10400.1/11392 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0022-247X 10.1016/j.jmaa.2006.01.069 |
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 |
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1799133263423340544 |