Maximal inequalities for a best approximation operator in Orlicz spaces

Autores
Favier, Sergio José; Zo, Felipe
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study a maximal operator Mf related with the best ϕ approximation by constants for a function f ∈ L ϕ 0 loc(ℝn), where we denote by ϕ 0 for the derivative function of the C1 convex function ϕ. We get a necessary and sufficient condition which assure strong inequalities of the type R ℝn θ(M|f|) dx ¬ K R ℝn θ(|f|) dx, where K is a constant independent of f. Some pointwise and mean convergence results are obtained. In the particular case ϕ(t) = t p+1 we obtain several equivalent conditions on the functions θ that assures strong inequalities of this type.
Fil: Favier, Sergio José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; Argentina
Fil: Zo, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; Argentina
Materia
Best Φ− Approximations by Constants
Extended Best Approximation Operator
Maximal Inequalities
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15554
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15554
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Maximal inequalities for a best approximation operator in Orlicz spacesFavier, Sergio JoséZo, FelipeBest Φ− Approximations by ConstantsExtended Best Approximation OperatorMaximal Inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study a maximal operator Mf related with the best ϕ approximation by constants for a function f ∈ L ϕ 0 loc(ℝn), where we denote by ϕ 0 for the derivative function of the C1 convex function ϕ. We get a necessary and sufficient condition which assure strong inequalities of the type R ℝn θ(M|f|) dx ¬ K R ℝn θ(|f|) dx, where K is a constant independent of f. Some pointwise and mean convergence results are obtained. In the particular case ϕ(t) = t p+1 we obtain several equivalent conditions on the functions θ that assures strong inequalities of this type.Fil: Favier, Sergio José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; ArgentinaFil: Zo, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; ArgentinaAdam Mickiewicz University in Poznań. Faculty of Mathematics and Computer Sciences2011-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15554Favier, Sergio José; Zo, Felipe; Maximal inequalities for a best approximation operator in Orlicz spaces; Adam Mickiewicz University in Poznań. Faculty of Mathematics and Computer Sciences; Commentationes Mathematicae; 51; 1; 8-2011; 3-212080-1211enginfo:eu-repo/semantics/altIdentifier/url/http://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/indexinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:39:20Zoai:ri.conicet.gov.ar:11336/15554instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 09:39:20.802CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Maximal inequalities for a best approximation operator in Orlicz spaces
title Maximal inequalities for a best approximation operator in Orlicz spaces
spellingShingle Maximal inequalities for a best approximation operator in Orlicz spaces
Favier, Sergio José
Best Φ− Approximations by Constants
Extended Best Approximation Operator
Maximal Inequalities
title_short Maximal inequalities for a best approximation operator in Orlicz spaces
title_full Maximal inequalities for a best approximation operator in Orlicz spaces
title_fullStr Maximal inequalities for a best approximation operator in Orlicz spaces
title_full_unstemmed Maximal inequalities for a best approximation operator in Orlicz spaces
title_sort Maximal inequalities for a best approximation operator in Orlicz spaces
dc.creator.none.fl_str_mv Favier, Sergio José
Zo, Felipe
author Favier, Sergio José
author_facet Favier, Sergio José
Zo, Felipe
author_role author
author2 Zo, Felipe
author2_role author
dc.subject.none.fl_str_mv Best Φ− Approximations by Constants
Extended Best Approximation Operator
Maximal Inequalities
topic Best Φ− Approximations by Constants
Extended Best Approximation Operator
Maximal Inequalities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study a maximal operator Mf related with the best ϕ approximation by constants for a function f ∈ L ϕ 0 loc(ℝn), where we denote by ϕ 0 for the derivative function of the C1 convex function ϕ. We get a necessary and sufficient condition which assure strong inequalities of the type R ℝn θ(M|f|) dx ¬ K R ℝn θ(|f|) dx, where K is a constant independent of f. Some pointwise and mean convergence results are obtained. In the particular case ϕ(t) = t p+1 we obtain several equivalent conditions on the functions θ that assures strong inequalities of this type.
Fil: Favier, Sergio José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; Argentina
Fil: Zo, Felipe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis ; Argentina
description In this paper we study a maximal operator Mf related with the best ϕ approximation by constants for a function f ∈ L ϕ 0 loc(ℝn), where we denote by ϕ 0 for the derivative function of the C1 convex function ϕ. We get a necessary and sufficient condition which assure strong inequalities of the type R ℝn θ(M|f|) dx ¬ K R ℝn θ(|f|) dx, where K is a constant independent of f. Some pointwise and mean convergence results are obtained. In the particular case ϕ(t) = t p+1 we obtain several equivalent conditions on the functions θ that assures strong inequalities of this type.
publishDate 2011
dc.date.none.fl_str_mv 2011-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/15554
Favier, Sergio José; Zo, Felipe; Maximal inequalities for a best approximation operator in Orlicz spaces; Adam Mickiewicz University in Poznań. Faculty of Mathematics and Computer Sciences; Commentationes Mathematicae; 51; 1; 8-2011; 3-21
2080-1211
url http://hdl.handle.net/11336/15554
identifier_str_mv Favier, Sergio José; Zo, Felipe; Maximal inequalities for a best approximation operator in Orlicz spaces; Adam Mickiewicz University in Poznań. Faculty of Mathematics and Computer Sciences; Commentationes Mathematicae; 51; 1; 8-2011; 3-21
2080-1211
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/index
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Adam Mickiewicz University in Poznań. Faculty of Mathematics and Computer Sciences
publisher.none.fl_str_mv Adam Mickiewicz University in Poznań. Faculty of Mathematics and Computer Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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