Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators

Autores
Bernardis, Ana Lucia; Lorente Dominguez, María
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator I+,k α,b and for the pairs of weights of the type (w, Mw), where w is any weight and M is a suitable one-sided maximal operator. We also prove that, for A+∞ weights, the operator I +,kα,b is controlled in the Lp (w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide a different way to obtain known results about the operators I +,kα,b. The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral I -,kα,b.
Fil: Bernardis, Ana Lucia. 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: Lorente Dominguez, María. 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
Commutators
Riemann-Liouville And Weyl Fractional Integrals
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:11336/84138
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operatorsBernardis, Ana LuciaLorente Dominguez, MaríaCommutatorsRiemann-Liouville And Weyl Fractional IntegralsWeighted Inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator I+,k α,b and for the pairs of weights of the type (w, Mw), where w is any weight and M is a suitable one-sided maximal operator. We also prove that, for A+∞ weights, the operator I +,kα,b is controlled in the Lp (w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide a different way to obtain known results about the operators I +,kα,b. The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral I -,kα,b.Fil: Bernardis, Ana Lucia. 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: Lorente Dominguez, María. 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 Ag2008-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84138Bernardis, Ana Lucia; Lorente Dominguez, María; Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 61; 4; 8-2008; 449-4750378-620XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-008-1600-yinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00020-008-1600-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:05:13Zoai:ri.conicet.gov.ar:11336/84138instacron: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 12:05:13.878CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
title Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
spellingShingle Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
Bernardis, Ana Lucia
Commutators
Riemann-Liouville And Weyl Fractional Integrals
Weighted Inequalities
title_short Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
title_full Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
title_fullStr Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
title_full_unstemmed Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
title_sort Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators
dc.creator.none.fl_str_mv Bernardis, Ana Lucia
Lorente Dominguez, María
author Bernardis, Ana Lucia
author_facet Bernardis, Ana Lucia
Lorente Dominguez, María
author_role author
author2 Lorente Dominguez, María
author2_role author
dc.subject.none.fl_str_mv Commutators
Riemann-Liouville And Weyl Fractional Integrals
Weighted Inequalities
topic Commutators
Riemann-Liouville And Weyl Fractional Integrals
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 Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator I+,k α,b and for the pairs of weights of the type (w, Mw), where w is any weight and M is a suitable one-sided maximal operator. We also prove that, for A+∞ weights, the operator I +,kα,b is controlled in the Lp (w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide a different way to obtain known results about the operators I +,kα,b. The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral I -,kα,b.
Fil: Bernardis, Ana Lucia. 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: Lorente Dominguez, María. 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 Let b be a BMO function, 0 < α < 1 and I+,k α,b the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator I+,k α,b and for the pairs of weights of the type (w, Mw), where w is any weight and M is a suitable one-sided maximal operator. We also prove that, for A+∞ weights, the operator I +,kα,b is controlled in the Lp (w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide a different way to obtain known results about the operators I +,kα,b. The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral I -,kα,b.
publishDate 2008
dc.date.none.fl_str_mv 2008-08
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/11336/84138
Bernardis, Ana Lucia; Lorente Dominguez, María; Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 61; 4; 8-2008; 449-475
0378-620X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84138
identifier_str_mv Bernardis, Ana Lucia; Lorente Dominguez, María; Sharp Two weight inequalities for commutators of Riemann-Liouville and Weyl fractional integral operators; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 61; 4; 8-2008; 449-475
0378-620X
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/s00020-008-1600-y
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00020-008-1600-y
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 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 12.982451

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