On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis

Autores
Aimar, Hugo Alejandro; Forzani, Liliana Maria; Scotto, Roberto Aníbal
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type independently of their orders.
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: Forzani, Liliana Maria. 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: Scotto, Roberto Aníbal. Universidad Nacional del Litoral; Argentina
Materia
Gaussian Measure
Maximal Functions
Singular Integrals
Hermie Expansions
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:11336/84070
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On Riesz transforms and maximal functions in the context of Gaussian harmonic analysisAimar, Hugo AlejandroForzani, Liliana MariaScotto, Roberto AníbalGaussian MeasureMaximal FunctionsSingular IntegralsHermie Expansionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type independently of their orders.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: Forzani, Liliana Maria. 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: Scotto, Roberto Aníbal. Universidad Nacional del Litoral; ArgentinaAmerican Mathematical Society2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84070Aimar, Hugo Alejandro; Forzani, Liliana Maria; Scotto, Roberto Aníbal; On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis; American Mathematical Society; Transactions Of The American Mathematical Society; 359; 5; 12-2007; 2137-21540002-9947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.2307/20161669info:eu-repo/semantics/altIdentifier/url/https://www.jstor.org/stable/20161669info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:10:39Zoai:ri.conicet.gov.ar:11336/84070instacron: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:34982025-10-15 15:10:39.683CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
title On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
spellingShingle On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
Aimar, Hugo Alejandro
Gaussian Measure
Maximal Functions
Singular Integrals
Hermie Expansions
title_short On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
title_full On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
title_fullStr On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
title_full_unstemmed On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
title_sort On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Forzani, Liliana Maria
Scotto, Roberto Aníbal
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Forzani, Liliana Maria
Scotto, Roberto Aníbal
author_role author
author2 Forzani, Liliana Maria
Scotto, Roberto Aníbal
author2_role author
author
dc.subject.none.fl_str_mv Gaussian Measure
Maximal Functions
Singular Integrals
Hermie Expansions
topic Gaussian Measure
Maximal Functions
Singular Integrals
Hermie Expansions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type independently of their orders.
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: Forzani, Liliana Maria. 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: Scotto, Roberto Aníbal. Universidad Nacional del Litoral; Argentina
description The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type independently of their orders.
publishDate 2007
dc.date.none.fl_str_mv 2007-12
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/11336/84070
Aimar, Hugo Alejandro; Forzani, Liliana Maria; Scotto, Roberto Aníbal; On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis; American Mathematical Society; Transactions Of The American Mathematical Society; 359; 5; 12-2007; 2137-2154
0002-9947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84070
identifier_str_mv Aimar, Hugo Alejandro; Forzani, Liliana Maria; Scotto, Roberto Aníbal; On Riesz transforms and maximal functions in the context of Gaussian harmonic analysis; American Mathematical Society; Transactions Of The American Mathematical Society; 359; 5; 12-2007; 2137-2154
0002-9947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.2307/20161669
info:eu-repo/semantics/altIdentifier/url/https://www.jstor.org/stable/20161669
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 13.22299

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