Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type
- Autores
- Bernardis, Ana Lucia; Hartzstein, Silvia Inés; Pradolini, Gladis Guadalupe
- Año de publicación
- 2006
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let 0 < γ < 1, b be a BMO function and Iγ, b m the commutator of order m for the fractional integral. We prove two type of weighted Lp inequalities for Iγ, b m in the context of the spaces of homogeneous type. The first one establishes that, for A∞ weights, the operator Iγ, b m is bounded in the weighted Lp norm by the maximal operator Mγ (Mm), where Mγ is the fractional maximal operator and Mm is the Hardy-Littlewood maximal operator iterated m times. The second inequality is a consequence of the first one and shows that the operator Iγ, b m is bounded from Lp [Mγ p (M[(m + 1) p] w) (x) d μ (x)] to Lp [w (x) d μ (x)], where [(m + 1) p] is the integer part of (m + 1) p and no condition on the weight w is required. From the first inequality we also obtain weighted Lp-Lq estimates for Iγ, b m generalizing the classical results of Muckenhoupt and Wheeden for the fractional integral operator.
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: Hartzstein, Silvia Inés. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Pradolini, Gladis Guadalupe. 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
Fractional Integral
Spaces of Homogeneous Type
Weighted Strong 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:11336/72959
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Weighted inequalities for commutators of fractional integrals on spaces of homogeneous typeBernardis, Ana LuciaHartzstein, Silvia InésPradolini, Gladis GuadalupeCommutatorsFractional IntegralSpaces of Homogeneous TypeWeighted Strong Inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let 0 < γ < 1, b be a BMO function and Iγ, b m the commutator of order m for the fractional integral. We prove two type of weighted Lp inequalities for Iγ, b m in the context of the spaces of homogeneous type. The first one establishes that, for A∞ weights, the operator Iγ, b m is bounded in the weighted Lp norm by the maximal operator Mγ (Mm), where Mγ is the fractional maximal operator and Mm is the Hardy-Littlewood maximal operator iterated m times. The second inequality is a consequence of the first one and shows that the operator Iγ, b m is bounded from Lp [Mγ p (M[(m + 1) p] w) (x) d μ (x)] to Lp [w (x) d μ (x)], where [(m + 1) p] is the integer part of (m + 1) p and no condition on the weight w is required. From the first inequality we also obtain weighted Lp-Lq estimates for Iγ, b m generalizing the classical results of Muckenhoupt and Wheeden for the fractional integral operator.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: Hartzstein, Silvia Inés. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Pradolini, Gladis Guadalupe. 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; ArgentinaAcademic Press Inc Elsevier Science2006-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/72959Bernardis, Ana Lucia; Hartzstein, Silvia Inés; Pradolini, Gladis Guadalupe; Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 322; 2; 10-2006; 825-8460022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2005.09.051info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X05009741info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:48:26Zoai:ri.conicet.gov.ar:11336/72959instacron: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 09:48:26.899CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
title |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
spellingShingle |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type Bernardis, Ana Lucia Commutators Fractional Integral Spaces of Homogeneous Type Weighted Strong Inequalities |
title_short |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
title_full |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
title_fullStr |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
title_full_unstemmed |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
title_sort |
Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type |
dc.creator.none.fl_str_mv |
Bernardis, Ana Lucia Hartzstein, Silvia Inés Pradolini, Gladis Guadalupe |
author |
Bernardis, Ana Lucia |
author_facet |
Bernardis, Ana Lucia Hartzstein, Silvia Inés Pradolini, Gladis Guadalupe |
author_role |
author |
author2 |
Hartzstein, Silvia Inés Pradolini, Gladis Guadalupe |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Commutators Fractional Integral Spaces of Homogeneous Type Weighted Strong Inequalities |
topic |
Commutators Fractional Integral Spaces of Homogeneous Type Weighted Strong 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 0 < γ < 1, b be a BMO function and Iγ, b m the commutator of order m for the fractional integral. We prove two type of weighted Lp inequalities for Iγ, b m in the context of the spaces of homogeneous type. The first one establishes that, for A∞ weights, the operator Iγ, b m is bounded in the weighted Lp norm by the maximal operator Mγ (Mm), where Mγ is the fractional maximal operator and Mm is the Hardy-Littlewood maximal operator iterated m times. The second inequality is a consequence of the first one and shows that the operator Iγ, b m is bounded from Lp [Mγ p (M[(m + 1) p] w) (x) d μ (x)] to Lp [w (x) d μ (x)], where [(m + 1) p] is the integer part of (m + 1) p and no condition on the weight w is required. From the first inequality we also obtain weighted Lp-Lq estimates for Iγ, b m generalizing the classical results of Muckenhoupt and Wheeden for the fractional integral operator. 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: Hartzstein, Silvia Inés. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina Fil: Pradolini, Gladis Guadalupe. 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 0 < γ < 1, b be a BMO function and Iγ, b m the commutator of order m for the fractional integral. We prove two type of weighted Lp inequalities for Iγ, b m in the context of the spaces of homogeneous type. The first one establishes that, for A∞ weights, the operator Iγ, b m is bounded in the weighted Lp norm by the maximal operator Mγ (Mm), where Mγ is the fractional maximal operator and Mm is the Hardy-Littlewood maximal operator iterated m times. The second inequality is a consequence of the first one and shows that the operator Iγ, b m is bounded from Lp [Mγ p (M[(m + 1) p] w) (x) d μ (x)] to Lp [w (x) d μ (x)], where [(m + 1) p] is the integer part of (m + 1) p and no condition on the weight w is required. From the first inequality we also obtain weighted Lp-Lq estimates for Iγ, b m generalizing the classical results of Muckenhoupt and Wheeden for the fractional integral operator. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006-10 |
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/11336/72959 Bernardis, Ana Lucia; Hartzstein, Silvia Inés; Pradolini, Gladis Guadalupe; Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 322; 2; 10-2006; 825-846 0022-247X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/72959 |
identifier_str_mv |
Bernardis, Ana Lucia; Hartzstein, Silvia Inés; Pradolini, Gladis Guadalupe; Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 322; 2; 10-2006; 825-846 0022-247X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2005.09.051 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X05009741 |
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 application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Academic Press Inc Elsevier Science |
publisher.none.fl_str_mv |
Academic Press Inc Elsevier 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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1844613504304152576 |
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13.070432 |