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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/84138
Ver los metadatos del registro completo
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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 Técnicas2025-10-22T12:05:13Zoai: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 |
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eng |
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eng |
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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 |
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openAccess |
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application/pdf application/pdf |
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Birkhauser Verlag Ag |
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Birkhauser Verlag Ag |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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