The Riesz potential as a multilinear operator into general BMOβ spaces

Autores
Aimar, Hugo Alejandro; Hartzstein, Silvia Inés; Iaffei, Bibiana Raquel; Viviani, Beatriz Eleonora
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that the target space is an adequate space BMOβ defined through mean oscillations. For general spaces of homogeneous type this is a Banach space of classes of functions modulii constants and the range of β is [0, 1). However, if X = ℝn (n ∈ N), we can extend the result to β > 0 taking in account that BMOβ is a space of classes modulii polynomials of order lower than or equal to [β]. Bibliography: 15 titles.
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: Hartzstein, Silvia Inés. Universidad Nacional del Litoral; Argentina
Fil: Iaffei, Bibiana Raquel. 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: 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
Riesz Potentials
Multilinear Operators
Lipschitz Integral Spaces
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:11336/84086
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Riesz potential as a multilinear operator into general BMOβ spacesAimar, Hugo AlejandroHartzstein, Silvia InésIaffei, Bibiana RaquelViviani, Beatriz EleonoraRiesz PotentialsMultilinear OperatorsLipschitz Integral Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that the target space is an adequate space BMOβ defined through mean oscillations. For general spaces of homogeneous type this is a Banach space of classes of functions modulii constants and the range of β is [0, 1). However, if X = ℝn (n ∈ N), we can extend the result to β > 0 taking in account that BMOβ is a space of classes modulii polynomials of order lower than or equal to [β]. Bibliography: 15 titles.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: Hartzstein, Silvia Inés. Universidad Nacional del Litoral; ArgentinaFil: Iaffei, Bibiana Raquel. 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: 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; ArgentinaSpringer Science2011-03info: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/11336/84086Aimar, Hugo Alejandro; Hartzstein, Silvia Inés; Iaffei, Bibiana Raquel; Viviani, Beatriz Eleonora; The Riesz potential as a multilinear operator into general BMOβ spaces; Springer Science; Journal Of Mathematical Sciences; 173; 6; 3-2011; 643-6551072-3374CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.springerlink.com/content/yp6636458k02121v/info:eu-repo/semantics/altIdentifier/doi/10.1007/s10958-011-0264-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:38:49Zoai:ri.conicet.gov.ar:11336/84086instacron: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:34982025-11-05 10:38:49.516CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Riesz potential as a multilinear operator into general BMOβ spaces
title The Riesz potential as a multilinear operator into general BMOβ spaces
spellingShingle The Riesz potential as a multilinear operator into general BMOβ spaces
Aimar, Hugo Alejandro
Riesz Potentials
Multilinear Operators
Lipschitz Integral Spaces
title_short The Riesz potential as a multilinear operator into general BMOβ spaces
title_full The Riesz potential as a multilinear operator into general BMOβ spaces
title_fullStr The Riesz potential as a multilinear operator into general BMOβ spaces
title_full_unstemmed The Riesz potential as a multilinear operator into general BMOβ spaces
title_sort The Riesz potential as a multilinear operator into general BMOβ spaces
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Hartzstein, Silvia Inés
Iaffei, Bibiana Raquel
Viviani, Beatriz Eleonora
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Hartzstein, Silvia Inés
Iaffei, Bibiana Raquel
Viviani, Beatriz Eleonora
author_role author
author2 Hartzstein, Silvia Inés
Iaffei, Bibiana Raquel
Viviani, Beatriz Eleonora
author2_role author
author
author
dc.subject.none.fl_str_mv Riesz Potentials
Multilinear Operators
Lipschitz Integral Spaces
topic Riesz Potentials
Multilinear Operators
Lipschitz Integral Spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that the target space is an adequate space BMOβ defined through mean oscillations. For general spaces of homogeneous type this is a Banach space of classes of functions modulii constants and the range of β is [0, 1). However, if X = ℝn (n ∈ N), we can extend the result to β > 0 taking in account that BMOβ is a space of classes modulii polynomials of order lower than or equal to [β]. Bibliography: 15 titles.
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: Hartzstein, Silvia Inés. Universidad Nacional del Litoral; Argentina
Fil: Iaffei, Bibiana Raquel. 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: 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 Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that the target space is an adequate space BMOβ defined through mean oscillations. For general spaces of homogeneous type this is a Banach space of classes of functions modulii constants and the range of β is [0, 1). However, if X = ℝn (n ∈ N), we can extend the result to β > 0 taking in account that BMOβ is a space of classes modulii polynomials of order lower than or equal to [β]. Bibliography: 15 titles.
publishDate 2011
dc.date.none.fl_str_mv 2011-03
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/11336/84086
Aimar, Hugo Alejandro; Hartzstein, Silvia Inés; Iaffei, Bibiana Raquel; Viviani, Beatriz Eleonora; The Riesz potential as a multilinear operator into general BMOβ spaces; Springer Science; Journal Of Mathematical Sciences; 173; 6; 3-2011; 643-655
1072-3374
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84086
identifier_str_mv Aimar, Hugo Alejandro; Hartzstein, Silvia Inés; Iaffei, Bibiana Raquel; Viviani, Beatriz Eleonora; The Riesz potential as a multilinear operator into general BMOβ spaces; Springer Science; Journal Of Mathematical Sciences; 173; 6; 3-2011; 643-655
1072-3374
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.springerlink.com/content/yp6636458k02121v/
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10958-011-0264-3
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 Springer Science
publisher.none.fl_str_mv Springer 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
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score 13.084122

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