The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform

Autores
Bernardis, Ana Lucia; Martín Reyes, F.J.
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all f ∈ Lp with p > 1/(1 + α) and −1 < α ≤ 0. The result does not hold for the space L1/(1 + α). In this paper we give a positive result for the smaller Lorentz space L1/(1 + α),1.
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, F.J.. Universidad de Málaga; España
Materia
Cesàro-α convergence
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:11336/98755
Acceder
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spelling The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transformBernardis, Ana LuciaMartín Reyes, F.J.Cesàro-α convergencehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all f ∈ Lp with p > 1/(1 + α) and −1 < α ≤ 0. The result does not hold for the space L1/(1 + α). In this paper we give a positive result for the smaller Lorentz space L1/(1 + α),1.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: Martín Reyes, F.J.. Universidad de Málaga; EspañaRoyal Society of Edinburgh2007-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98755Bernardis, Ana Lucia; Martín Reyes, F.J.; The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform; Royal Society of Edinburgh; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 130; 2; 7-2007; 225-2370308-2105CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0308210500000123info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:24Zoai:ri.conicet.gov.ar:11336/98755instacron: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 09:38:24.784CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
title The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
spellingShingle The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
Bernardis, Ana Lucia
Cesàro-α convergence
title_short The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
title_full The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
title_fullStr The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
title_full_unstemmed The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
title_sort The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform
dc.creator.none.fl_str_mv Bernardis, Ana Lucia
Martín Reyes, F.J.
author Bernardis, Ana Lucia
author_facet Bernardis, Ana Lucia
Martín Reyes, F.J.
author_role author
author2 Martín Reyes, F.J.
author2_role author
dc.subject.none.fl_str_mv Cesàro-α convergence
topic Cesàro-α convergence
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all f ∈ Lp with p > 1/(1 + α) and −1 < α ≤ 0. The result does not hold for the space L1/(1 + α). In this paper we give a positive result for the smaller Lorentz space L1/(1 + α),1.
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, F.J.. Universidad de Málaga; España
description Recently, Sarrión and the authors gave a sufficient condition on invertible Lamperti operators on Lp which guarantees the convergence in the Cesàro-α sense of the ergodic averages and the ergodic Hilbert transform for all f ∈ Lp with p > 1/(1 + α) and −1 < α ≤ 0. The result does not hold for the space L1/(1 + α). In this paper we give a positive result for the smaller Lorentz space L1/(1 + α),1.
publishDate 2007
dc.date.none.fl_str_mv 2007-07
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/11336/98755
Bernardis, Ana Lucia; Martín Reyes, F.J.; The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform; Royal Society of Edinburgh; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 130; 2; 7-2007; 225-237
0308-2105
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98755
identifier_str_mv Bernardis, Ana Lucia; Martín Reyes, F.J.; The limit case of the Cesàro-α convergence of the ergodic averages and the ergodic Hilbert transform; Royal Society of Edinburgh; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 130; 2; 7-2007; 225-237
0308-2105
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1017/S0308210500000123
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 Royal Society of Edinburgh
publisher.none.fl_str_mv Royal Society of Edinburgh
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 13.070432

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