Riesz transforms for laguerre expansions

Autores
Harboure, Eleonor Ofelia; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p < ∞. We achieve this result by taking advantage of the existing classical relationship between n-variable Hermite polynomials and Laguerre polynomials on the half line of type α = n/2 - 1. Such connection allows us to transfer known boundedness properties for Hermite operators to Laguerre operators corresponding to those specific values of α. To extend the results to any α > -1, we make use of transplantation and some weighted inequalities we obtain in the Hermite setting (which we believe of independent interest).
Fil: Harboure, Eleonor Ofelia. 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: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; España
Fil: Viviani, Beatriz Eleonora. 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
Materia
Laguerre Functions Systems
Riesz Transforms
Weighted Inequalities
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:11336/84074
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Riesz transforms for laguerre expansionsHarboure, Eleonor OfeliaTorrea Hernández, José LuisViviani, Beatriz EleonoraLaguerre Functions SystemsRiesz TransformsWeighted Inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p < ∞. We achieve this result by taking advantage of the existing classical relationship between n-variable Hermite polynomials and Laguerre polynomials on the half line of type α = n/2 - 1. Such connection allows us to transfer known boundedness properties for Hermite operators to Laguerre operators corresponding to those specific values of α. To extend the results to any α > -1, we make use of transplantation and some weighted inequalities we obtain in the Hermite setting (which we believe of independent interest).Fil: Harboure, Eleonor Ofelia. 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: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; EspañaFil: Viviani, Beatriz Eleonora. 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; ArgentinaIndiana University2006-12info: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/11336/84074Harboure, Eleonor Ofelia; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; Riesz transforms for laguerre expansions; Indiana University; Indiana University Mathematics Journal; 55; 3; 12-2006; 999-10140022-2518CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1512/iumj.2006.55.2650info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:51:46Zoai:ri.conicet.gov.ar:11336/84074instacron: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:34982025-11-12 09:51:46.673CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Riesz transforms for laguerre expansions
title Riesz transforms for laguerre expansions
spellingShingle Riesz transforms for laguerre expansions
Harboure, Eleonor Ofelia
Laguerre Functions Systems
Riesz Transforms
Weighted Inequalities
title_short Riesz transforms for laguerre expansions
title_full Riesz transforms for laguerre expansions
title_fullStr Riesz transforms for laguerre expansions
title_full_unstemmed Riesz transforms for laguerre expansions
title_sort Riesz transforms for laguerre expansions
dc.creator.none.fl_str_mv Harboure, Eleonor Ofelia
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author Harboure, Eleonor Ofelia
author_facet Harboure, Eleonor Ofelia
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author_role author
author2 Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author2_role author
author
dc.subject.none.fl_str_mv Laguerre Functions Systems
Riesz Transforms
Weighted Inequalities
topic Laguerre Functions Systems
Riesz Transforms
Weighted Inequalities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p < ∞. We achieve this result by taking advantage of the existing classical relationship between n-variable Hermite polynomials and Laguerre polynomials on the half line of type α = n/2 - 1. Such connection allows us to transfer known boundedness properties for Hermite operators to Laguerre operators corresponding to those specific values of α. To extend the results to any α > -1, we make use of transplantation and some weighted inequalities we obtain in the Hermite setting (which we believe of independent interest).
Fil: Harboure, Eleonor Ofelia. 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: Torrea Hernández, José Luis. Universidad Autónoma de Madrid; España
Fil: Viviani, Beatriz Eleonora. 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
description We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p < ∞. We achieve this result by taking advantage of the existing classical relationship between n-variable Hermite polynomials and Laguerre polynomials on the half line of type α = n/2 - 1. Such connection allows us to transfer known boundedness properties for Hermite operators to Laguerre operators corresponding to those specific values of α. To extend the results to any α > -1, we make use of transplantation and some weighted inequalities we obtain in the Hermite setting (which we believe of independent interest).
publishDate 2006
dc.date.none.fl_str_mv 2006-12
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/11336/84074
Harboure, Eleonor Ofelia; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; Riesz transforms for laguerre expansions; Indiana University; Indiana University Mathematics Journal; 55; 3; 12-2006; 999-1014
0022-2518
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84074
identifier_str_mv Harboure, Eleonor Ofelia; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; Riesz transforms for laguerre expansions; Indiana University; Indiana University Mathematics Journal; 55; 3; 12-2006; 999-1014
0022-2518
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1512/iumj.2006.55.2650
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 Indiana University
publisher.none.fl_str_mv Indiana University
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 12.976206

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