Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden

Autores
Lerner, Andrei K.; Ombrosi, Sheldy Javier; Pérez, Carlos
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w.
Fil: Lerner, Andrei K.. Universidad de Sevilla; España
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
Fil: Pérez, Carlos. Universidad de Sevilla; España
Materia
Calderon
Zygmund Operators
Weights
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:11336/79545
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-WheedenLerner, Andrei K.Ombrosi, Sheldy JavierPérez, CarlosCalderonZygmund OperatorsWeightshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w.Fil: Lerner, Andrei K.. Universidad de Sevilla; EspañaFil: 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; ArgentinaFil: Pérez, Carlos. Universidad de Sevilla; EspañaBirkhäuser Publishing2009-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/79545Lerner, Andrei K.; Ombrosi, Sheldy Javier; Pérez, Carlos; Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden; Birkhäuser Publishing; Journal Of Fourier Analysis And Applications; 15; 3; 6-2009; 394-4031069-58691531-5851CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00041-008-9032-2info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-008-9032-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:33:21Zoai:ri.conicet.gov.ar:11336/79545instacron: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 09:33:22.102CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
title Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
spellingShingle Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
Lerner, Andrei K.
Calderon
Zygmund Operators
Weights
title_short Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
title_full Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
title_fullStr Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
title_full_unstemmed Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
title_sort Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
dc.creator.none.fl_str_mv Lerner, Andrei K.
Ombrosi, Sheldy Javier
Pérez, Carlos
author Lerner, Andrei K.
author_facet Lerner, Andrei K.
Ombrosi, Sheldy Javier
Pérez, Carlos
author_role author
author2 Ombrosi, Sheldy Javier
Pérez, Carlos
author2_role author
author
dc.subject.none.fl_str_mv Calderon
Zygmund Operators
Weights
topic Calderon
Zygmund Operators
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 A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w.
Fil: Lerner, Andrei K.. Universidad de Sevilla; España
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
Fil: Pérez, Carlos. Universidad de Sevilla; España
description A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w.
publishDate 2009
dc.date.none.fl_str_mv 2009-06
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/11336/79545
Lerner, Andrei K.; Ombrosi, Sheldy Javier; Pérez, Carlos; Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden; Birkhäuser Publishing; Journal Of Fourier Analysis And Applications; 15; 3; 6-2009; 394-403
1069-5869
1531-5851
CONICET Digital
CONICET
url http://hdl.handle.net/11336/79545
identifier_str_mv Lerner, Andrei K.; Ombrosi, Sheldy Javier; Pérez, Carlos; Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden; Birkhäuser Publishing; Journal Of Fourier Analysis And Applications; 15; 3; 6-2009; 394-403
1069-5869
1531-5851
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://link.springer.com/article/10.1007/s00041-008-9032-2
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-008-9032-2
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 Birkhäuser Publishing
publisher.none.fl_str_mv Birkhäuser Publishing
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 13.070432

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