Calderón weights as Muckenhoupt weights

Autores
Duoandikoextea, Javier; Martín Reyes, Francisco Javier; Ombrosi, Sheldy Javier
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on L p(w) are the Calderón weights of the class Cp. We prove a characterization of the weights in Cp by a single condition which allows us to see that Cp is the class of Muckenhoupt weights associated with a maximal operator defined through a basis in (0,∞). The same condition characterizes the weighted weak-type inequalities for 1 < p < ∞, but that the weights for the strong type and the weak type differ for p = 1. We also prove that the weights in Cp do not behave like the usual Ap weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.
Fil: Duoandikoextea, Javier. Universidad del Pais Vasco; España
Fil: Martín Reyes, Francisco Javier. Universidad de Malaga; 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
Materia
CALDERÓN OPERATOR
MAXIMAL OPERATOR
MUCKENHOUPT BASES
WEIGHTED 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:11336/11929
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/11929
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Calderón weights as Muckenhoupt weightsDuoandikoextea, JavierMartín Reyes, Francisco JavierOmbrosi, Sheldy JavierCALDERÓN OPERATORMAXIMAL OPERATORMUCKENHOUPT BASESWEIGHTED INEQUALITIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on L p(w) are the Calderón weights of the class Cp. We prove a characterization of the weights in Cp by a single condition which allows us to see that Cp is the class of Muckenhoupt weights associated with a maximal operator defined through a basis in (0,∞). The same condition characterizes the weighted weak-type inequalities for 1 < p < ∞, but that the weights for the strong type and the weak type differ for p = 1. We also prove that the weights in Cp do not behave like the usual Ap weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.Fil: Duoandikoextea, Javier. Universidad del Pais Vasco; EspañaFil: Martín Reyes, Francisco Javier. Universidad de Malaga; 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; ArgentinaIndiana University2013-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/11929Duoandikoextea, Javier; Martín Reyes, Francisco Javier; Ombrosi, Sheldy Javier; Calderón weights as Muckenhoupt weights; Indiana University; Indiana University Mathematics Journal; 62; 3; 9-2013; 891-9100022-2518enginfo:eu-repo/semantics/altIdentifier/url/http://www.iumj.indiana.edu/oai/2013/62/4971/4971.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:58:46Zoai:ri.conicet.gov.ar:11336/11929instacron: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 09:58:46.518CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Calderón weights as Muckenhoupt weights
title Calderón weights as Muckenhoupt weights
spellingShingle Calderón weights as Muckenhoupt weights
Duoandikoextea, Javier
CALDERÓN OPERATOR
MAXIMAL OPERATOR
MUCKENHOUPT BASES
WEIGHTED INEQUALITIES
title_short Calderón weights as Muckenhoupt weights
title_full Calderón weights as Muckenhoupt weights
title_fullStr Calderón weights as Muckenhoupt weights
title_full_unstemmed Calderón weights as Muckenhoupt weights
title_sort Calderón weights as Muckenhoupt weights
dc.creator.none.fl_str_mv Duoandikoextea, Javier
Martín Reyes, Francisco Javier
Ombrosi, Sheldy Javier
author Duoandikoextea, Javier
author_facet Duoandikoextea, Javier
Martín Reyes, Francisco Javier
Ombrosi, Sheldy Javier
author_role author
author2 Martín Reyes, Francisco Javier
Ombrosi, Sheldy Javier
author2_role author
author
dc.subject.none.fl_str_mv CALDERÓN OPERATOR
MAXIMAL OPERATOR
MUCKENHOUPT BASES
WEIGHTED INEQUALITIES
topic CALDERÓN OPERATOR
MAXIMAL OPERATOR
MUCKENHOUPT BASES
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 The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on L p(w) are the Calderón weights of the class Cp. We prove a characterization of the weights in Cp by a single condition which allows us to see that Cp is the class of Muckenhoupt weights associated with a maximal operator defined through a basis in (0,∞). The same condition characterizes the weighted weak-type inequalities for 1 < p < ∞, but that the weights for the strong type and the weak type differ for p = 1. We also prove that the weights in Cp do not behave like the usual Ap weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.
Fil: Duoandikoextea, Javier. Universidad del Pais Vasco; España
Fil: Martín Reyes, Francisco Javier. Universidad de Malaga; 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
description The Calderón operator S is the sum of the the Hardy averaging operator and its adjoint. The weights w for which S is bounded on L p(w) are the Calderón weights of the class Cp. We prove a characterization of the weights in Cp by a single condition which allows us to see that Cp is the class of Muckenhoupt weights associated with a maximal operator defined through a basis in (0,∞). The same condition characterizes the weighted weak-type inequalities for 1 < p < ∞, but that the weights for the strong type and the weak type differ for p = 1. We also prove that the weights in Cp do not behave like the usual Ap weights with respect to some properties and, in particular, we answer an open question on extrapolation for Muckenhoupt bases without the openness property.
publishDate 2013
dc.date.none.fl_str_mv 2013-09
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/11336/11929
Duoandikoextea, Javier; Martín Reyes, Francisco Javier; Ombrosi, Sheldy Javier; Calderón weights as Muckenhoupt weights; Indiana University; Indiana University Mathematics Journal; 62; 3; 9-2013; 891-910
0022-2518
url http://hdl.handle.net/11336/11929
identifier_str_mv Duoandikoextea, Javier; Martín Reyes, Francisco Javier; Ombrosi, Sheldy Javier; Calderón weights as Muckenhoupt weights; Indiana University; Indiana University Mathematics Journal; 62; 3; 9-2013; 891-910
0022-2518
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.iumj.indiana.edu/oai/2013/62/4971/4971.xml
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 Indiana University
publisher.none.fl_str_mv Indiana University
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
_version_ 1842269540222763008
score 13.13397

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