Weighted mixed weak-type inequalities for multilinear operators

Autores
Li, Kangwe; Ombrosi, Sheldy Javier; Picardi, María Belén
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present a theorem that generalizes Sawyer’s classic result about mixed weighted inequalities to the multilinear context. Let ~w = (w1, ..., wm) and ν = w 1 m 1 ...w 1 mm , the main result of the paper sentences that under different conditions on the weights we can obtain T ( ~f )(x) v L 1m ,∞(νv 1m ) ≤ C Ym i=1 kfikL1(wi), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M, and also for M(f~)(x): the multi(sub)linear maximal function introduced in [13]. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder´on-Zygmund operators.
Fil: Li, Kangwe. Basque Center Applied Mathematics; 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: Picardi, María Belén. 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
MULTILINEAR OPERATORS
MIXED 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:11336/86012
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/86012
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Weighted mixed weak-type inequalities for multilinear operatorsLi, KangweOmbrosi, Sheldy JavierPicardi, María BelénMULTILINEAR OPERATORSMIXED WEIGHTED INEQUALITIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we present a theorem that generalizes Sawyer’s classic result about mixed weighted inequalities to the multilinear context. Let ~w = (w1, ..., wm) and ν = w 1 m 1 ...w 1 mm , the main result of the paper sentences that under different conditions on the weights we can obtain T ( ~f )(x) v L 1m ,∞(νv 1m ) ≤ C Ym i=1 kfikL1(wi), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M, and also for M(f~)(x): the multi(sub)linear maximal function introduced in [13]. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder´on-Zygmund operators.Fil: Li, Kangwe. Basque Center Applied Mathematics; 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: Picardi, María Belén. 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; ArgentinaPolish Academy of Sciences. Institute of Mathematics2018-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/86012Li, Kangwe; Ombrosi, Sheldy Javier; Picardi, María Belén; Weighted mixed weak-type inequalities for multilinear operators; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 244; 5-2018; 203-2150039-3223CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1705.09206info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/244/2/112487/weighted-mixed-weak-type-inequalities-for-multilinear-operatorsinfo:eu-repo/semantics/altIdentifier/doi/10.4064/sm170529-31-8info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:45:27Zoai:ri.conicet.gov.ar:11336/86012instacron: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 09:45:27.406CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weighted mixed weak-type inequalities for multilinear operators
title Weighted mixed weak-type inequalities for multilinear operators
spellingShingle Weighted mixed weak-type inequalities for multilinear operators
Li, Kangwe
MULTILINEAR OPERATORS
MIXED WEIGHTED INEQUALITIES
title_short Weighted mixed weak-type inequalities for multilinear operators
title_full Weighted mixed weak-type inequalities for multilinear operators
title_fullStr Weighted mixed weak-type inequalities for multilinear operators
title_full_unstemmed Weighted mixed weak-type inequalities for multilinear operators
title_sort Weighted mixed weak-type inequalities for multilinear operators
dc.creator.none.fl_str_mv Li, Kangwe
Ombrosi, Sheldy Javier
Picardi, María Belén
author Li, Kangwe
author_facet Li, Kangwe
Ombrosi, Sheldy Javier
Picardi, María Belén
author_role author
author2 Ombrosi, Sheldy Javier
Picardi, María Belén
author2_role author
author
dc.subject.none.fl_str_mv MULTILINEAR OPERATORS
MIXED WEIGHTED INEQUALITIES
topic MULTILINEAR OPERATORS
MIXED 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 In this paper we present a theorem that generalizes Sawyer’s classic result about mixed weighted inequalities to the multilinear context. Let ~w = (w1, ..., wm) and ν = w 1 m 1 ...w 1 mm , the main result of the paper sentences that under different conditions on the weights we can obtain T ( ~f )(x) v L 1m ,∞(νv 1m ) ≤ C Ym i=1 kfikL1(wi), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M, and also for M(f~)(x): the multi(sub)linear maximal function introduced in [13]. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder´on-Zygmund operators.
Fil: Li, Kangwe. Basque Center Applied Mathematics; 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: Picardi, María Belén. 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 In this paper we present a theorem that generalizes Sawyer’s classic result about mixed weighted inequalities to the multilinear context. Let ~w = (w1, ..., wm) and ν = w 1 m 1 ...w 1 mm , the main result of the paper sentences that under different conditions on the weights we can obtain T ( ~f )(x) v L 1m ,∞(νv 1m ) ≤ C Ym i=1 kfikL1(wi), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M, and also for M(f~)(x): the multi(sub)linear maximal function introduced in [13]. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder´on-Zygmund operators.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
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/11336/86012
Li, Kangwe; Ombrosi, Sheldy Javier; Picardi, María Belén; Weighted mixed weak-type inequalities for multilinear operators; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 244; 5-2018; 203-215
0039-3223
CONICET Digital
CONICET
url http://hdl.handle.net/11336/86012
identifier_str_mv Li, Kangwe; Ombrosi, Sheldy Javier; Picardi, María Belén; Weighted mixed weak-type inequalities for multilinear operators; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 244; 5-2018; 203-215
0039-3223
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://arxiv.org/abs/1705.09206
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/244/2/112487/weighted-mixed-weak-type-inequalities-for-multilinear-operators
info:eu-repo/semantics/altIdentifier/doi/10.4064/sm170529-31-8
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 Polish Academy of Sciences. Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
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_ 1842268732642033664
score 13.13397

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