Multiparameter ergodic Cesàro-α averages

Autores
Bernardis, Ana Lucia; Crescimbeni, Raquel Liliana; Ferrari Freire, Cecilia
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏j=1kAαj−1nj−ijTikk⋯Ti11f. For these averages we prove the almost everywhere convergence on X and the convergence in the Lp(ν) norm, when n1,…,nk→∞ independently, for all f∈Lp(dν) with p>1/α∗ where α∗=min1≤j≤kαj. In the limit case p=1/α∗, we prove that the averages Rnˉ,αˉf converge almost everywhere on X for all f in the Orlicz–Lorentz space Λ(1/α∗,φm−1) with φm(t)=t(1+log+t)m. To obtain the result in the limit case we need to study inequalities for the composition of operators Ti that are of restricted weak type (pi,pi). As another application of these inequalities we also study the strong Cesàro-αˉ continuity of functions.
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; Argentina
Fil: Ferrari Freire, Cecilia. Universidad Nacional del Comahue; Argentina
Materia
MULTIPARAMETER
ERGODIC
CESARO
AVERAGES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/30776

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spelling Multiparameter ergodic Cesàro-α averagesBernardis, Ana LuciaCrescimbeni, Raquel LilianaFerrari Freire, CeciliaMULTIPARAMETERERGODICCESAROAVERAGEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏j=1kAαj−1nj−ijTikk⋯Ti11f. For these averages we prove the almost everywhere convergence on X and the convergence in the Lp(ν) norm, when n1,…,nk→∞ independently, for all f∈Lp(dν) with p>1/α∗ where α∗=min1≤j≤kαj. In the limit case p=1/α∗, we prove that the averages Rnˉ,αˉf converge almost everywhere on X for all f in the Orlicz–Lorentz space Λ(1/α∗,φm−1) with φm(t)=t(1+log+t)m. To obtain the result in the limit case we need to study inequalities for the composition of operators Ti that are of restricted weak type (pi,pi). As another application of these inequalities we also study the strong Cesàro-αˉ continuity of functions.Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; ArgentinaFil: Ferrari Freire, Cecilia. Universidad Nacional del Comahue; ArgentinaPolish Academy of Sciences. Institute of Mathematics2015-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/30776Ferrari Freire, Cecilia; Crescimbeni, Raquel Liliana; Bernardis, Ana Lucia; Multiparameter ergodic Cesàro-α averages; Polish Academy of Sciences. Institute of Mathematics; Colloquium Mathematicum; 140; 3-2015; 15-290010-1354CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4064/cm140-1-3info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/140/1/87538/multiparameter-ergodic-cesaro-alpha-averagesinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:54:45Zoai:ri.conicet.gov.ar:11336/30776instacron: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:34982025-09-03 09:54:45.748CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multiparameter ergodic Cesàro-α averages
title Multiparameter ergodic Cesàro-α averages
spellingShingle Multiparameter ergodic Cesàro-α averages
Bernardis, Ana Lucia
MULTIPARAMETER
ERGODIC
CESARO
AVERAGES
title_short Multiparameter ergodic Cesàro-α averages
title_full Multiparameter ergodic Cesàro-α averages
title_fullStr Multiparameter ergodic Cesàro-α averages
title_full_unstemmed Multiparameter ergodic Cesàro-α averages
title_sort Multiparameter ergodic Cesàro-α averages
dc.creator.none.fl_str_mv Bernardis, Ana Lucia
Crescimbeni, Raquel Liliana
Ferrari Freire, Cecilia
author Bernardis, Ana Lucia
author_facet Bernardis, Ana Lucia
Crescimbeni, Raquel Liliana
Ferrari Freire, Cecilia
author_role author
author2 Crescimbeni, Raquel Liliana
Ferrari Freire, Cecilia
author2_role author
author
dc.subject.none.fl_str_mv MULTIPARAMETER
ERGODIC
CESARO
AVERAGES
topic MULTIPARAMETER
ERGODIC
CESARO
AVERAGES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏j=1kAαj−1nj−ijTikk⋯Ti11f. For these averages we prove the almost everywhere convergence on X and the convergence in the Lp(ν) norm, when n1,…,nk→∞ independently, for all f∈Lp(dν) with p>1/α∗ where α∗=min1≤j≤kαj. In the limit case p=1/α∗, we prove that the averages Rnˉ,αˉf converge almost everywhere on X for all f in the Orlicz–Lorentz space Λ(1/α∗,φm−1) with φm(t)=t(1+log+t)m. To obtain the result in the limit case we need to study inequalities for the composition of operators Ti that are of restricted weak type (pi,pi). As another application of these inequalities we also study the strong Cesàro-αˉ continuity of functions.
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue; Argentina
Fil: Ferrari Freire, Cecilia. Universidad Nacional del Comahue; Argentina
description Let (X,F,ν) be a σ-finite measure space. Associated with k Lamperti operators on Lp(ν), T1,…,Tk, nˉ=(n1,…,nk)∈Nk and αˉ=(α1,…,αk) with 0<αj≤1, we define the ergodic Cesàro-αˉ averages Rnˉ,αˉf=1∏kj=1Aαjnj∑ik=0nk⋯∑i1=0n1∏j=1kAαj−1nj−ijTikk⋯Ti11f. For these averages we prove the almost everywhere convergence on X and the convergence in the Lp(ν) norm, when n1,…,nk→∞ independently, for all f∈Lp(dν) with p>1/α∗ where α∗=min1≤j≤kαj. In the limit case p=1/α∗, we prove that the averages Rnˉ,αˉf converge almost everywhere on X for all f in the Orlicz–Lorentz space Λ(1/α∗,φm−1) with φm(t)=t(1+log+t)m. To obtain the result in the limit case we need to study inequalities for the composition of operators Ti that are of restricted weak type (pi,pi). As another application of these inequalities we also study the strong Cesàro-αˉ continuity of functions.
publishDate 2015
dc.date.none.fl_str_mv 2015-03
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/11336/30776
Ferrari Freire, Cecilia; Crescimbeni, Raquel Liliana; Bernardis, Ana Lucia; Multiparameter ergodic Cesàro-α averages; Polish Academy of Sciences. Institute of Mathematics; Colloquium Mathematicum; 140; 3-2015; 15-29
0010-1354
CONICET Digital
CONICET
url http://hdl.handle.net/11336/30776
identifier_str_mv Ferrari Freire, Cecilia; Crescimbeni, Raquel Liliana; Bernardis, Ana Lucia; Multiparameter ergodic Cesàro-α averages; Polish Academy of Sciences. Institute of Mathematics; Colloquium Mathematicum; 140; 3-2015; 15-29
0010-1354
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4064/cm140-1-3
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/140/1/87538/multiparameter-ergodic-cesaro-alpha-averages
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
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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