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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/84138
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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 Técnicas2025-09-29T10:32:45Zoai: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:34982025-09-29 10:32:46.253CONICET 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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13.070432 |