An extrapolation theorem with applications to weighted estimates for singular integrals

Autores
Lerner, Andrei K.; Ombrosi, Sheldy Javier
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove an extrapolation theorem saying that the weighted weak type (1; 1) inequality for A1 weights implies the strong Lp(w) bound in terms of the Lp(w) operator norm of the maximal operator M. The weak Muchkenhoupt-Wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a Calder´on-Zygmund operator T for any p > 1: ∥T∥ Lp(w) ≤ c∥M∥p Lp(w): The latter conjecture would yield the sharp estimates for ∥T∥ Lp(w) in terms of the Aq characteristic of w for any 1 < q < p. In this paper we get a weaker inequality ∥T∥ Lp(w) ≤ c∥M∥p Lp(w) log(1 + ∥M∥ Lp(w)) with the corresponding estimates for ∥w∥Aq when 1 < q < p.
Fil: Lerner, Andrei K.. Bar Ilan University; Israel
Fil: Ombrosi, Sheldy Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
Extrapolation
Integrals
Weights
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/66250
Acceder
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network_name_str CONICET Digital (CONICET)
spelling An extrapolation theorem with applications to weighted estimates for singular integralsLerner, Andrei K.Ombrosi, Sheldy JavierExtrapolationIntegralsWeightshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove an extrapolation theorem saying that the weighted weak type (1; 1) inequality for A1 weights implies the strong Lp(w) bound in terms of the Lp(w) operator norm of the maximal operator M. The weak Muchkenhoupt-Wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a Calder´on-Zygmund operator T for any p > 1: ∥T∥ Lp(w) ≤ c∥M∥p Lp(w): The latter conjecture would yield the sharp estimates for ∥T∥ Lp(w) in terms of the Aq characteristic of w for any 1 < q < p. In this paper we get a weaker inequality ∥T∥ Lp(w) ≤ c∥M∥p Lp(w) log(1 + ∥M∥ Lp(w)) with the corresponding estimates for ∥w∥Aq when 1 < q < p.Fil: Lerner, Andrei K.. Bar Ilan University; IsraelFil: Ombrosi, Sheldy Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaAcademic Press Inc Elsevier Science2012-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/66250Lerner, Andrei K.; Ombrosi, Sheldy Javier; An extrapolation theorem with applications to weighted estimates for singular integrals; Academic Press Inc Elsevier Science; Journal Of Functional Analysis; 262; 10; 5-2012; 4475-44870022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022123612001000info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2012.02.025info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:09Zoai:ri.conicet.gov.ar:11336/66250instacron: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:34982025-09-03 09:56:09.821CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An extrapolation theorem with applications to weighted estimates for singular integrals
title An extrapolation theorem with applications to weighted estimates for singular integrals
spellingShingle An extrapolation theorem with applications to weighted estimates for singular integrals
Lerner, Andrei K.
Extrapolation
Integrals
Weights
title_short An extrapolation theorem with applications to weighted estimates for singular integrals
title_full An extrapolation theorem with applications to weighted estimates for singular integrals
title_fullStr An extrapolation theorem with applications to weighted estimates for singular integrals
title_full_unstemmed An extrapolation theorem with applications to weighted estimates for singular integrals
title_sort An extrapolation theorem with applications to weighted estimates for singular integrals
dc.creator.none.fl_str_mv Lerner, Andrei K.
Ombrosi, Sheldy Javier
author Lerner, Andrei K.
author_facet Lerner, Andrei K.
Ombrosi, Sheldy Javier
author_role author
author2 Ombrosi, Sheldy Javier
author2_role author
dc.subject.none.fl_str_mv Extrapolation
Integrals
Weights
topic Extrapolation
Integrals
Weights
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove an extrapolation theorem saying that the weighted weak type (1; 1) inequality for A1 weights implies the strong Lp(w) bound in terms of the Lp(w) operator norm of the maximal operator M. The weak Muchkenhoupt-Wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a Calder´on-Zygmund operator T for any p > 1: ∥T∥ Lp(w) ≤ c∥M∥p Lp(w): The latter conjecture would yield the sharp estimates for ∥T∥ Lp(w) in terms of the Aq characteristic of w for any 1 < q < p. In this paper we get a weaker inequality ∥T∥ Lp(w) ≤ c∥M∥p Lp(w) log(1 + ∥M∥ Lp(w)) with the corresponding estimates for ∥w∥Aq when 1 < q < p.
Fil: Lerner, Andrei K.. Bar Ilan University; Israel
Fil: Ombrosi, Sheldy Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description We prove an extrapolation theorem saying that the weighted weak type (1; 1) inequality for A1 weights implies the strong Lp(w) bound in terms of the Lp(w) operator norm of the maximal operator M. The weak Muchkenhoupt-Wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a Calder´on-Zygmund operator T for any p > 1: ∥T∥ Lp(w) ≤ c∥M∥p Lp(w): The latter conjecture would yield the sharp estimates for ∥T∥ Lp(w) in terms of the Aq characteristic of w for any 1 < q < p. In this paper we get a weaker inequality ∥T∥ Lp(w) ≤ c∥M∥p Lp(w) log(1 + ∥M∥ Lp(w)) with the corresponding estimates for ∥w∥Aq when 1 < q < p.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
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/11336/66250
Lerner, Andrei K.; Ombrosi, Sheldy Javier; An extrapolation theorem with applications to weighted estimates for singular integrals; Academic Press Inc Elsevier Science; Journal Of Functional Analysis; 262; 10; 5-2012; 4475-4487
0022-1236
CONICET Digital
CONICET
url http://hdl.handle.net/11336/66250
identifier_str_mv Lerner, Andrei K.; Ombrosi, Sheldy Javier; An extrapolation theorem with applications to weighted estimates for singular integrals; Academic Press Inc Elsevier Science; Journal Of Functional Analysis; 262; 10; 5-2012; 4475-4487
0022-1236
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022123612001000
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2012.02.025
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv 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 13.13397

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