The rho-variation as an operator between maximal operators and singular integrals

Autores
Crescimbeni, Raquel Liliana; Macias, Roberto Aristobulo; Menarguez, Teresa; Torrea, Jose Luis; Viviani, Beatriz Eleonora
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The ρ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. Δ and −Δ + |x|2) are proved to be bounded from Lp(Rn w(x)dx) into itself (fromL1(Rn w(x)dx) into weak-L1(Rn w(x)dx) in the case p = 1) for 1 ≤ p < ∞ and w being a weight in the Muckenhoupt?s Ap class. In the case p = ∞ it is proved that these operators do not map L∞ into itself. Even more, they map L∞ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.
Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue. Facultad de Economía y Administración. Departamento de Matemática; Argentina
Fil: Macias, Roberto Aristobulo. 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: Menarguez, Teresa. Universidad Autónoma de Madrid. Facultad de Ciencias; España
Fil: Torrea, Jose Luis. Universidad Autónoma de Madrid. Facultad de Ciencias; 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
Heat
Oscillation
Poisson
Variation
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:11336/84079
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84079
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The rho-variation as an operator between maximal operators and singular integralsCrescimbeni, Raquel LilianaMacias, Roberto AristobuloMenarguez, TeresaTorrea, Jose LuisViviani, Beatriz EleonoraHeatOscillationPoissonVariationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The ρ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. Δ and −Δ + |x|2) are proved to be bounded from Lp(Rn w(x)dx) into itself (fromL1(Rn w(x)dx) into weak-L1(Rn w(x)dx) in the case p = 1) for 1 ≤ p < ∞ and w being a weight in the Muckenhoupt?s Ap class. In the case p = ∞ it is proved that these operators do not map L∞ into itself. Even more, they map L∞ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue. Facultad de Economía y Administración. Departamento de Matemática; ArgentinaFil: Macias, Roberto Aristobulo. 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: Menarguez, Teresa. Universidad Autónoma de Madrid. Facultad de Ciencias; EspañaFil: Torrea, Jose Luis. Universidad Autónoma de Madrid. Facultad de Ciencias; 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; ArgentinaBirkhauser Verlag Ag2009-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84079Crescimbeni, Raquel Liliana; Macias, Roberto Aristobulo; Menarguez, Teresa; Torrea, Jose Luis; Viviani, Beatriz Eleonora; The rho-variation as an operator between maximal operators and singular integrals; Birkhauser Verlag Ag; Journal Of Evolution Equations; 9; 1; 3-2009; 81-1021424-3199CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00028-009-0003-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:54:40Zoai:ri.conicet.gov.ar:11336/84079instacron: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:34982025-09-03 09:54:41.139CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The rho-variation as an operator between maximal operators and singular integrals
title The rho-variation as an operator between maximal operators and singular integrals
spellingShingle The rho-variation as an operator between maximal operators and singular integrals
Crescimbeni, Raquel Liliana
Heat
Oscillation
Poisson
Variation
title_short The rho-variation as an operator between maximal operators and singular integrals
title_full The rho-variation as an operator between maximal operators and singular integrals
title_fullStr The rho-variation as an operator between maximal operators and singular integrals
title_full_unstemmed The rho-variation as an operator between maximal operators and singular integrals
title_sort The rho-variation as an operator between maximal operators and singular integrals
dc.creator.none.fl_str_mv Crescimbeni, Raquel Liliana
Macias, Roberto Aristobulo
Menarguez, Teresa
Torrea, Jose Luis
Viviani, Beatriz Eleonora
author Crescimbeni, Raquel Liliana
author_facet Crescimbeni, Raquel Liliana
Macias, Roberto Aristobulo
Menarguez, Teresa
Torrea, Jose Luis
Viviani, Beatriz Eleonora
author_role author
author2 Macias, Roberto Aristobulo
Menarguez, Teresa
Torrea, Jose Luis
Viviani, Beatriz Eleonora
author2_role author
author
author
author
dc.subject.none.fl_str_mv Heat
Oscillation
Poisson
Variation
topic Heat
Oscillation
Poisson
Variation
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 ρ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. Δ and −Δ + |x|2) are proved to be bounded from Lp(Rn w(x)dx) into itself (fromL1(Rn w(x)dx) into weak-L1(Rn w(x)dx) in the case p = 1) for 1 ≤ p < ∞ and w being a weight in the Muckenhoupt?s Ap class. In the case p = ∞ it is proved that these operators do not map L∞ into itself. Even more, they map L∞ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.
Fil: Crescimbeni, Raquel Liliana. Universidad Nacional del Comahue. Facultad de Economía y Administración. Departamento de Matemática; Argentina
Fil: Macias, Roberto Aristobulo. 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: Menarguez, Teresa. Universidad Autónoma de Madrid. Facultad de Ciencias; España
Fil: Torrea, Jose Luis. Universidad Autónoma de Madrid. Facultad de Ciencias; 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 The ρ-variation and the oscillation of the heat and Poisson semigroups of the Laplacian and Hermite operators (i.e. Δ and −Δ + |x|2) are proved to be bounded from Lp(Rn w(x)dx) into itself (fromL1(Rn w(x)dx) into weak-L1(Rn w(x)dx) in the case p = 1) for 1 ≤ p < ∞ and w being a weight in the Muckenhoupt?s Ap class. In the case p = ∞ it is proved that these operators do not map L∞ into itself. Even more, they map L∞ into BMO but the range of the image is strictly smaller that the range of a general singular integral operator.
publishDate 2009
dc.date.none.fl_str_mv 2009-03
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/11336/84079
Crescimbeni, Raquel Liliana; Macias, Roberto Aristobulo; Menarguez, Teresa; Torrea, Jose Luis; Viviani, Beatriz Eleonora; The rho-variation as an operator between maximal operators and singular integrals; Birkhauser Verlag Ag; Journal Of Evolution Equations; 9; 1; 3-2009; 81-102
1424-3199
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84079
identifier_str_mv Crescimbeni, Raquel Liliana; Macias, Roberto Aristobulo; Menarguez, Teresa; Torrea, Jose Luis; Viviani, Beatriz Eleonora; The rho-variation as an operator between maximal operators and singular integrals; Birkhauser Verlag Ag; Journal Of Evolution Equations; 9; 1; 3-2009; 81-102
1424-3199
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/s00028-009-0003-0
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
dc.publisher.none.fl_str_mv Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
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 13.13397

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