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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/72959
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/72959
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-10-22T11:17:25Zoai: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:34982025-10-22 11:17:25.558CONICET 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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score 12.982451

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