Lp-dimension free boundedness for Riesz transforms associated to Hermite functions

Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L^p(R^d ), 1 < p < ∞ . In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not depending on...

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Autores: Harboure, Eleonor Ofelia, Rosa, L. de, Segovia Fernandez, Carlos, Torrea Hernández, José Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2004
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/101031
Acceso en línea:http://hdl.handle.net/11336/101031
Access Level:acceso abierto
Palabra clave:Hermite functions
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Lp-dimension free boundedness for Riesz transforms associated to Hermite functionsHarboure, Eleonor OfeliaRosa, L. deSegovia Fernandez, CarlosTorrea Hernández, José LuisHermite functionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L^p(R^d ), 1 < p < ∞ . In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not depending on the dimension d. Moreover, we define Riesz transforms of higher order and free dimensional estimates of the L^p-bounds of these operators are obtained. In order to prove the mentioned results we give an extension of the Littlewood-Paley theory that we believe of independent interest.Fil: Harboure, Eleonor Ofelia. Universidad Nacional del Litoral. Facultad de Ingeniería Química. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Rosa, L. de. Universidad de Buenos Aires; ArgentinaFil: Segovia Fernandez, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; EspañaSpringer2004-04info: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/11336/101031Harboure, Eleonor Ofelia; Rosa, L. de; Segovia Fernandez, Carlos; Torrea Hernández, José Luis; Lp-dimension free boundedness for Riesz transforms associated to Hermite functions; Springer; Mathematische Annalen; 328; 4; 4-2004; 653-6820025-5831CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00208-003-0501-2info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00208-003-0501-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:40:05Zoai:ri.conicet.gov.ar:11336/101031instacron: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:34982024-05-08 13:40:05.324CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
spellingShingle Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
Harboure, Eleonor Ofelia
Hermite functions
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_full Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_fullStr Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_full_unstemmed Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
title_sort Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
dc.creator.none.fl_str_mv Harboure, Eleonor Ofelia
Rosa, L. de
Segovia Fernandez, Carlos
Torrea Hernández, José Luis
author Harboure, Eleonor Ofelia
author_facet Harboure, Eleonor Ofelia
Rosa, L. de
Segovia Fernandez, Carlos
Torrea Hernández, José Luis
author_role author
author2 Rosa, L. de
Segovia Fernandez, Carlos
Torrea Hernández, José Luis
author2_role author
author
author
dc.subject.none.fl_str_mv Hermite functions
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Hermite functions
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L^p(R^d ), 1 < p < ∞ . In this paper we give a different proof that allows us to show that the Lp-norms of these operators are bounded by a constant not depending on the dimension d. Moreover, we define Riesz transforms of higher order and free dimensional estimates of the L^p-bounds of these operators are obtained. In order to prove the mentioned results we give an extension of the Littlewood-Paley theory that we believe of independent interest.
publishDate 2004
dc.date.none.fl_str_mv 2004-04
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/11336/101031
Harboure, Eleonor Ofelia; Rosa, L. de; Segovia Fernandez, Carlos; Torrea Hernández, José Luis; Lp-dimension free boundedness for Riesz transforms associated to Hermite functions; Springer; Mathematische Annalen; 328; 4; 4-2004; 653-682
0025-5831
CONICET Digital
CONICET
url http://hdl.handle.net/11336/101031
identifier_str_mv Harboure, Eleonor Ofelia; Rosa, L. de; Segovia Fernandez, Carlos; Torrea Hernández, José Luis; Lp-dimension free boundedness for Riesz transforms associated to Hermite functions; Springer; Mathematische Annalen; 328; 4; 4-2004; 653-682
0025-5831
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00208-003-0501-2
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00208-003-0501-2
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 Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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