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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/30776
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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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13.13397 |