A sharp weighted transplantation theorem for Laguerre function expansions

Autores
Garrigós, G.; Harboure, Eleonor Ofelia; Signes, T.; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We find the sharp range of boundedness for transplantation operators associated with Laguerre function expansions in Lp spaces with power weights. Namely, the operators interchanging {Lkα} and {Lkβ} are bounded in Lp (yδ p) if and only if - frac(ρ, 2) - frac(1, p) < δ < 1 - frac(1, p) + frac(ρ, 2), where ρ = min {α, β}. This improves a previous partial result by Stempak and Trebels, which was only sharp for ρ ≤ 0. Our approach is based on new multiplier estimates for Hermite expansions, weighted inequalities for local singular integrals and a careful analysis of Kanjin's original proof of the unweighted case. As a consequence we obtain new results on multipliers, Riesz transforms and g-functions for Laguerre expansions in Lp (yδ p).
Fil: Garrigós, G.. Universidad Autónoma de Madrid; España
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: Signes, T.. Universidad de Murcia; España
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 Function
Weighted Inequalities
Transplantation Theorem
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:11336/84071
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84071
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A sharp weighted transplantation theorem for Laguerre function expansionsGarrigós, G.Harboure, Eleonor OfeliaSignes, T.Torrea Hernández, José LuisViviani, Beatriz EleonoraLaguerre FunctionWeighted InequalitiesTransplantation Theoremhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We find the sharp range of boundedness for transplantation operators associated with Laguerre function expansions in Lp spaces with power weights. Namely, the operators interchanging {Lkα} and {Lkβ} are bounded in Lp (yδ p) if and only if - frac(ρ, 2) - frac(1, p) < δ < 1 - frac(1, p) + frac(ρ, 2), where ρ = min {α, β}. This improves a previous partial result by Stempak and Trebels, which was only sharp for ρ ≤ 0. Our approach is based on new multiplier estimates for Hermite expansions, weighted inequalities for local singular integrals and a careful analysis of Kanjin's original proof of the unweighted case. As a consequence we obtain new results on multipliers, Riesz transforms and g-functions for Laguerre expansions in Lp (yδ p).Fil: Garrigós, G.. Universidad Autónoma de Madrid; EspañaFil: 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: Signes, T.. Universidad de Murcia; EspañaFil: 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; ArgentinaAcademic Press Inc Elsevier Science2007-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84071Garrigós, G.; Harboure, Eleonor Ofelia; Signes, T.; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; A sharp weighted transplantation theorem for Laguerre function expansions; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 244; 1; 3-2007; 247-2760022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2006.11.019info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:10:04Zoai:ri.conicet.gov.ar:11336/84071instacron: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:34982025-10-22 11:10:04.346CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A sharp weighted transplantation theorem for Laguerre function expansions
title A sharp weighted transplantation theorem for Laguerre function expansions
spellingShingle A sharp weighted transplantation theorem for Laguerre function expansions
Garrigós, G.
Laguerre Function
Weighted Inequalities
Transplantation Theorem
title_short A sharp weighted transplantation theorem for Laguerre function expansions
title_full A sharp weighted transplantation theorem for Laguerre function expansions
title_fullStr A sharp weighted transplantation theorem for Laguerre function expansions
title_full_unstemmed A sharp weighted transplantation theorem for Laguerre function expansions
title_sort A sharp weighted transplantation theorem for Laguerre function expansions
dc.creator.none.fl_str_mv Garrigós, G.
Harboure, Eleonor Ofelia
Signes, T.
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author Garrigós, G.
author_facet Garrigós, G.
Harboure, Eleonor Ofelia
Signes, T.
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author_role author
author2 Harboure, Eleonor Ofelia
Signes, T.
Torrea Hernández, José Luis
Viviani, Beatriz Eleonora
author2_role author
author
author
author
dc.subject.none.fl_str_mv Laguerre Function
Weighted Inequalities
Transplantation Theorem
topic Laguerre Function
Weighted Inequalities
Transplantation Theorem
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 find the sharp range of boundedness for transplantation operators associated with Laguerre function expansions in Lp spaces with power weights. Namely, the operators interchanging {Lkα} and {Lkβ} are bounded in Lp (yδ p) if and only if - frac(ρ, 2) - frac(1, p) < δ < 1 - frac(1, p) + frac(ρ, 2), where ρ = min {α, β}. This improves a previous partial result by Stempak and Trebels, which was only sharp for ρ ≤ 0. Our approach is based on new multiplier estimates for Hermite expansions, weighted inequalities for local singular integrals and a careful analysis of Kanjin's original proof of the unweighted case. As a consequence we obtain new results on multipliers, Riesz transforms and g-functions for Laguerre expansions in Lp (yδ p).
Fil: Garrigós, G.. Universidad Autónoma de Madrid; España
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: Signes, T.. Universidad de Murcia; España
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 find the sharp range of boundedness for transplantation operators associated with Laguerre function expansions in Lp spaces with power weights. Namely, the operators interchanging {Lkα} and {Lkβ} are bounded in Lp (yδ p) if and only if - frac(ρ, 2) - frac(1, p) < δ < 1 - frac(1, p) + frac(ρ, 2), where ρ = min {α, β}. This improves a previous partial result by Stempak and Trebels, which was only sharp for ρ ≤ 0. Our approach is based on new multiplier estimates for Hermite expansions, weighted inequalities for local singular integrals and a careful analysis of Kanjin's original proof of the unweighted case. As a consequence we obtain new results on multipliers, Riesz transforms and g-functions for Laguerre expansions in Lp (yδ p).
publishDate 2007
dc.date.none.fl_str_mv 2007-03
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/11336/84071
Garrigós, G.; Harboure, Eleonor Ofelia; Signes, T.; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; A sharp weighted transplantation theorem for Laguerre function expansions; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 244; 1; 3-2007; 247-276
0022-1236
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84071
identifier_str_mv Garrigós, G.; Harboure, Eleonor Ofelia; Signes, T.; Torrea Hernández, José Luis; Viviani, Beatriz Eleonora; A sharp weighted transplantation theorem for Laguerre function expansions; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 244; 1; 3-2007; 247-276
0022-1236
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2006.11.019
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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_ 1846781457333223424
score 12.982451

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