A unified point of view on boundedness of Riesz type potentials

Autores
Iaffei, Bibiana Raquel; Nitti, Rosa Liliana
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce a natural extension of the Riesz potentials to quasimetricmeasure spaces with an upper doubling measure. In particular, theseoperators are defined when the underlying space has components of differingdimensions. We study the behavior of the potential on classical and variableexponent Lebesgue spaces, obtaining necessary and sufficient conditions forits boundedness. The technique we use relies on a geometric property ofthe measure of the balls which holds both in the doubling and non-doublingsituations, and allows us to present our results in a unified way.
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: Nitti, Rosa Liliana. 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
Operators on function spaces
Function spaces arising in harmonic analysis
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:11336/68091
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/68091
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network_name_str CONICET Digital (CONICET)
spelling A unified point of view on boundedness of Riesz type potentialsIaffei, Bibiana RaquelNitti, Rosa LilianaOperators on function spacesFunction spaces arising in harmonic analysishttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce a natural extension of the Riesz potentials to quasimetricmeasure spaces with an upper doubling measure. In particular, theseoperators are defined when the underlying space has components of differingdimensions. We study the behavior of the potential on classical and variableexponent Lebesgue spaces, obtaining necessary and sufficient conditions forits boundedness. The technique we use relies on a geometric property ofthe measure of the balls which holds both in the doubling and non-doublingsituations, and allows us to present our results in a unified way.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; ArgentinaFil: Nitti, Rosa Liliana. 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; ArgentinaUnión Matemática Argentina2018-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68091Iaffei, Bibiana Raquel; Nitti, Rosa Liliana; A unified point of view on boundedness of Riesz type potentials; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 1; 8-2018; 99-1210041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v59n1/v59n1a05.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:26:48Zoai:ri.conicet.gov.ar:11336/68091instacron: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:34982025-10-15 15:26:49.132CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A unified point of view on boundedness of Riesz type potentials
title A unified point of view on boundedness of Riesz type potentials
spellingShingle A unified point of view on boundedness of Riesz type potentials
Iaffei, Bibiana Raquel
Operators on function spaces
Function spaces arising in harmonic analysis
title_short A unified point of view on boundedness of Riesz type potentials
title_full A unified point of view on boundedness of Riesz type potentials
title_fullStr A unified point of view on boundedness of Riesz type potentials
title_full_unstemmed A unified point of view on boundedness of Riesz type potentials
title_sort A unified point of view on boundedness of Riesz type potentials
dc.creator.none.fl_str_mv Iaffei, Bibiana Raquel
Nitti, Rosa Liliana
author Iaffei, Bibiana Raquel
author_facet Iaffei, Bibiana Raquel
Nitti, Rosa Liliana
author_role author
author2 Nitti, Rosa Liliana
author2_role author
dc.subject.none.fl_str_mv Operators on function spaces
Function spaces arising in harmonic analysis
topic Operators on function spaces
Function spaces arising in harmonic analysis
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 introduce a natural extension of the Riesz potentials to quasimetricmeasure spaces with an upper doubling measure. In particular, theseoperators are defined when the underlying space has components of differingdimensions. We study the behavior of the potential on classical and variableexponent Lebesgue spaces, obtaining necessary and sufficient conditions forits boundedness. The technique we use relies on a geometric property ofthe measure of the balls which holds both in the doubling and non-doublingsituations, and allows us to present our results in a unified way.
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: Nitti, Rosa Liliana. 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 introduce a natural extension of the Riesz potentials to quasimetricmeasure spaces with an upper doubling measure. In particular, theseoperators are defined when the underlying space has components of differingdimensions. We study the behavior of the potential on classical and variableexponent Lebesgue spaces, obtaining necessary and sufficient conditions forits boundedness. The technique we use relies on a geometric property ofthe measure of the balls which holds both in the doubling and non-doublingsituations, and allows us to present our results in a unified way.
publishDate 2018
dc.date.none.fl_str_mv 2018-08
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/11336/68091
Iaffei, Bibiana Raquel; Nitti, Rosa Liliana; A unified point of view on boundedness of Riesz type potentials; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 1; 8-2018; 99-121
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68091
identifier_str_mv Iaffei, Bibiana Raquel; Nitti, Rosa Liliana; A unified point of view on boundedness of Riesz type potentials; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 1; 8-2018; 99-121
0041-6932
1669-9637
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://inmabb.criba.edu.ar/revuma/pdf/v59n1/v59n1a05.pdf
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 Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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 13.22299

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