Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/12104 |
Resumo: | In connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w,x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions. The main results contain necessary and sufficient conditions, in terms of lower and upper bounds of indices m(w, x) and M(w, x), for the uniform belongness of functions w(., r) to Zygmund-Bary-Stechkin classes. We give also applications to local dimensions in metric measure spaces and characterization of some integral inequalities involving radial weights and measures of balls in such spaces. |
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Parameter depending almost monotonic functions and their applications to dimensions in metric measure spacesSingular Integral-OperatorsSpherical PotentialsComplex-OrderHolder SpacesIn connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w,x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions. The main results contain necessary and sufficient conditions, in terms of lower and upper bounds of indices m(w, x) and M(w, x), for the uniform belongness of functions w(., r) to Zygmund-Bary-Stechkin classes. We give also applications to local dimensions in metric measure spaces and characterization of some integral inequalities involving radial weights and measures of balls in such spaces.FCT, Portugal [SFRH/BPD/34258/2006]; INTAS project "Variable Exponent Analysis" [06-1000017-8792]Scientific HorizonSapientiaSamko, Natasha2018-12-07T14:58:35Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/12104eng0972-680210.1155/2009/929041info: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:RCAAP2023-07-24T10:24:02Zoai:sapientia.ualg.pt:10400.1/12104Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:03:30.462400Repositório 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 |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
title |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
spellingShingle |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces Samko, Natasha Singular Integral-Operators Spherical Potentials Complex-Order Holder Spaces |
title_short |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
title_full |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
title_fullStr |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
title_full_unstemmed |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
title_sort |
Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces |
author |
Samko, Natasha |
author_facet |
Samko, Natasha |
author_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Samko, Natasha |
dc.subject.por.fl_str_mv |
Singular Integral-Operators Spherical Potentials Complex-Order Holder Spaces |
topic |
Singular Integral-Operators Spherical Potentials Complex-Order Holder Spaces |
description |
In connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w,x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions. The main results contain necessary and sufficient conditions, in terms of lower and upper bounds of indices m(w, x) and M(w, x), for the uniform belongness of functions w(., r) to Zygmund-Bary-Stechkin classes. We give also applications to local dimensions in metric measure spaces and characterization of some integral inequalities involving radial weights and measures of balls in such spaces. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 2009-01-01T00:00:00Z 2018-12-07T14:58:35Z |
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/10400.1/12104 |
url |
http://hdl.handle.net/10400.1/12104 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0972-6802 10.1155/2009/929041 |
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 |
Scientific Horizon |
publisher.none.fl_str_mv |
Scientific Horizon |
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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1799133269817556992 |