Ergodic transforms associated to general averages

Autores
Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in Lp, 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in Lp. For p = 1 we find that the maximal ergodic transforms are of weak type (1,1). Convergence results are also proved. We give some general examples of Cesàro bounded semigroups.
Fil: Aimar, Hugo Alejandro. 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: 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: Martín Reyes, Francisco Javier. Universidad de Málaga; España
Materia
Abel Means
Averages
Ces&Agrave;
Ergodic Transforms
Ro Averages
Ro Bounded Semigroups
Weighted Inequalities
Weights
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:11336/75195
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/75195
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Ergodic transforms associated to general averagesAimar, Hugo AlejandroBernardis, Ana LuciaMartín Reyes, Francisco JavierAbel MeansAveragesCes&Agrave;Ergodic TransformsRo AveragesRo Bounded SemigroupsWeighted InequalitiesWeightshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in Lp, 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in Lp. For p = 1 we find that the maximal ergodic transforms are of weak type (1,1). Convergence results are also proved. We give some general examples of Cesàro bounded semigroups.Fil: Aimar, Hugo Alejandro. 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: 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: Martín Reyes, Francisco Javier. Universidad de Málaga; EspañaPolish Academy of Sciences. Institute of Mathematics2010-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/75195Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Ergodic transforms associated to general averages; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 199; 2; 5-2010; 107-1430039-3223CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4064/sm199-2-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:37Zoai:ri.conicet.gov.ar:11336/75195instacron: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:34982025-09-29 09:33:37.596CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Ergodic transforms associated to general averages
title Ergodic transforms associated to general averages
spellingShingle Ergodic transforms associated to general averages
Aimar, Hugo Alejandro
Abel Means
Averages
Ces&Agrave;
Ergodic Transforms
Ro Averages
Ro Bounded Semigroups
Weighted Inequalities
Weights
title_short Ergodic transforms associated to general averages
title_full Ergodic transforms associated to general averages
title_fullStr Ergodic transforms associated to general averages
title_full_unstemmed Ergodic transforms associated to general averages
title_sort Ergodic transforms associated to general averages
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Bernardis, Ana Lucia
Martín Reyes, Francisco Javier
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Bernardis, Ana Lucia
Martín Reyes, Francisco Javier
author_role author
author2 Bernardis, Ana Lucia
Martín Reyes, Francisco Javier
author2_role author
author
dc.subject.none.fl_str_mv Abel Means
Averages
Ces&Agrave;
Ergodic Transforms
Ro Averages
Ro Bounded Semigroups
Weighted Inequalities
Weights
topic Abel Means
Averages
Ces&Agrave;
Ergodic Transforms
Ro Averages
Ro Bounded Semigroups
Weighted Inequalities
Weights
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in Lp, 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in Lp. For p = 1 we find that the maximal ergodic transforms are of weak type (1,1). Convergence results are also proved. We give some general examples of Cesàro bounded semigroups.
Fil: Aimar, Hugo Alejandro. 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: 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: Martín Reyes, Francisco Javier. Universidad de Málaga; España
description Jones and Rosenblatt started the study of an ergodic transform which is analogous to the martingale transform. In this paper we present a unified treatment of the ergodic transforms associated to positive groups induced by nonsingular flows and to general means which include the usual averages, Cesàro-α averages and Abel means. We prove the boundedness in Lp, 1 < p < ∞, of the maximal ergodic transforms assuming that the semigroup is Cesàro bounded in Lp. For p = 1 we find that the maximal ergodic transforms are of weak type (1,1). Convergence results are also proved. We give some general examples of Cesàro bounded semigroups.
publishDate 2010
dc.date.none.fl_str_mv 2010-05
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/11336/75195
Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Ergodic transforms associated to general averages; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 199; 2; 5-2010; 107-143
0039-3223
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75195
identifier_str_mv Aimar, Hugo Alejandro; Bernardis, Ana Lucia; Martín Reyes, Francisco Javier; Ergodic transforms associated to general averages; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 199; 2; 5-2010; 107-143
0039-3223
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/sm199-2-1
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
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
_version_ 1844613034090168320
score 13.070432

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