Weighted Norm Inequalities for Rough Singular Integral Operators

Autores
Kangwei, Li; Pérez, Carlos; Rivera Ríos, Israel Pablo; Roncal, Luz
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals TΩ with Ω ∈ L∞(Sn-1) and the Bochner–Riesz multiplier at the critical index B(n-1)/2. More precisely, we prove qualitative and quantitative versions of Coifman–Fefferman type inequalities and their vector-valued extensions, weighted Ap- A∞ strong and weak type inequalities for 1 < p< ∞, and A1- A∞ type weak (1, 1) estimates. Moreover, Fefferman–Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 1990s. As a corollary, we obtain the weighted A1- A∞ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function Ω ∈ Lq(Sn-1) , 1 < q< ∞, and provide Fefferman–Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde–Alonso et al. (Anal PDE 10(5):1255–1284, 2017), results by the first author (Collect Math 68:129–144, 2017), suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for A∞ weights (Cruz-Uribe et al. in J Funct Anal 213:412–439, 2004, Curbera et al. in Adv Math 203:256–318, 2006), and ideas contained in previous works by Seeger (J Am Math Soc 9:95–105 1996) and Fan and Sato (Tohoku Math J 53:265–284, 2001).
Fil: Kangwei, Li. Basque Center for Applied Mathematics; España
Fil: Pérez, Carlos. Universidad del País Vasco; España
Fil: Rivera Ríos, Israel Pablo. 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. Universidad del País Vasco; España
Fil: Roncal, Luz. Basque Center for Applied Mathematics; España
Materia
FEFFERMAN–STEIN INEQUALITIES
ROUGH OPERATORS
RUBIO DE FRANCIA ALGORITHM
SPARSE 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:11336/85550
Acceder
id CONICETDig_8bd7384d435fc290b0bd4e0ccb0ed777
oai_identifier_str oai:ri.conicet.gov.ar:11336/85550
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Weighted Norm Inequalities for Rough Singular Integral OperatorsKangwei, LiPérez, CarlosRivera Ríos, Israel PabloRoncal, LuzFEFFERMAN–STEIN INEQUALITIESROUGH OPERATORSRUBIO DE FRANCIA ALGORITHMSPARSE OPERATORSWEIGHTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals TΩ with Ω ∈ L∞(Sn-1) and the Bochner–Riesz multiplier at the critical index B(n-1)/2. More precisely, we prove qualitative and quantitative versions of Coifman–Fefferman type inequalities and their vector-valued extensions, weighted Ap- A∞ strong and weak type inequalities for 1 < p< ∞, and A1- A∞ type weak (1, 1) estimates. Moreover, Fefferman–Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 1990s. As a corollary, we obtain the weighted A1- A∞ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function Ω ∈ Lq(Sn-1) , 1 < q< ∞, and provide Fefferman–Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde–Alonso et al. (Anal PDE 10(5):1255–1284, 2017), results by the first author (Collect Math 68:129–144, 2017), suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for A∞ weights (Cruz-Uribe et al. in J Funct Anal 213:412–439, 2004, Curbera et al. in Adv Math 203:256–318, 2006), and ideas contained in previous works by Seeger (J Am Math Soc 9:95–105 1996) and Fan and Sato (Tohoku Math J 53:265–284, 2001).Fil: Kangwei, Li. Basque Center for Applied Mathematics; EspañaFil: Pérez, Carlos. Universidad del País Vasco; EspañaFil: Rivera Ríos, Israel Pablo. 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. Universidad del País Vasco; EspañaFil: Roncal, Luz. Basque Center for Applied Mathematics; EspañaSpringer2019-07info: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/11336/85550Kangwei, Li; Pérez, Carlos; Rivera Ríos, Israel Pablo; Roncal, Luz; Weighted Norm Inequalities for Rough Singular Integral Operators; Springer; The Journal Of Geometric Analysis; 29; 3; 7-2019; 2526-25641050-69261559-002XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs12220-018-0085-4info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-018-0085-4info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1701.05170info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:22Zoai:ri.conicet.gov.ar:11336/85550instacron: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 09:50:22.956CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weighted Norm Inequalities for Rough Singular Integral Operators
title Weighted Norm Inequalities for Rough Singular Integral Operators
spellingShingle Weighted Norm Inequalities for Rough Singular Integral Operators
Kangwei, Li
FEFFERMAN–STEIN INEQUALITIES
ROUGH OPERATORS
RUBIO DE FRANCIA ALGORITHM
SPARSE OPERATORS
WEIGHTS
title_short Weighted Norm Inequalities for Rough Singular Integral Operators
title_full Weighted Norm Inequalities for Rough Singular Integral Operators
title_fullStr Weighted Norm Inequalities for Rough Singular Integral Operators
title_full_unstemmed Weighted Norm Inequalities for Rough Singular Integral Operators
title_sort Weighted Norm Inequalities for Rough Singular Integral Operators
dc.creator.none.fl_str_mv Kangwei, Li
Pérez, Carlos
Rivera Ríos, Israel Pablo
Roncal, Luz
author Kangwei, Li
author_facet Kangwei, Li
Pérez, Carlos
Rivera Ríos, Israel Pablo
Roncal, Luz
author_role author
author2 Pérez, Carlos
Rivera Ríos, Israel Pablo
Roncal, Luz
author2_role author
author
author
dc.subject.none.fl_str_mv FEFFERMAN–STEIN INEQUALITIES
ROUGH OPERATORS
RUBIO DE FRANCIA ALGORITHM
SPARSE OPERATORS
WEIGHTS
topic FEFFERMAN–STEIN INEQUALITIES
ROUGH OPERATORS
RUBIO DE FRANCIA ALGORITHM
SPARSE 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 In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals TΩ with Ω ∈ L∞(Sn-1) and the Bochner–Riesz multiplier at the critical index B(n-1)/2. More precisely, we prove qualitative and quantitative versions of Coifman–Fefferman type inequalities and their vector-valued extensions, weighted Ap- A∞ strong and weak type inequalities for 1 < p< ∞, and A1- A∞ type weak (1, 1) estimates. Moreover, Fefferman–Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 1990s. As a corollary, we obtain the weighted A1- A∞ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function Ω ∈ Lq(Sn-1) , 1 < q< ∞, and provide Fefferman–Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde–Alonso et al. (Anal PDE 10(5):1255–1284, 2017), results by the first author (Collect Math 68:129–144, 2017), suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for A∞ weights (Cruz-Uribe et al. in J Funct Anal 213:412–439, 2004, Curbera et al. in Adv Math 203:256–318, 2006), and ideas contained in previous works by Seeger (J Am Math Soc 9:95–105 1996) and Fan and Sato (Tohoku Math J 53:265–284, 2001).
Fil: Kangwei, Li. Basque Center for Applied Mathematics; España
Fil: Pérez, Carlos. Universidad del País Vasco; España
Fil: Rivera Ríos, Israel Pablo. 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. Universidad del País Vasco; España
Fil: Roncal, Luz. Basque Center for Applied Mathematics; España
description In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals TΩ with Ω ∈ L∞(Sn-1) and the Bochner–Riesz multiplier at the critical index B(n-1)/2. More precisely, we prove qualitative and quantitative versions of Coifman–Fefferman type inequalities and their vector-valued extensions, weighted Ap- A∞ strong and weak type inequalities for 1 < p< ∞, and A1- A∞ type weak (1, 1) estimates. Moreover, Fefferman–Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 1990s. As a corollary, we obtain the weighted A1- A∞ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function Ω ∈ Lq(Sn-1) , 1 < q< ∞, and provide Fefferman–Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde–Alonso et al. (Anal PDE 10(5):1255–1284, 2017), results by the first author (Collect Math 68:129–144, 2017), suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for A∞ weights (Cruz-Uribe et al. in J Funct Anal 213:412–439, 2004, Curbera et al. in Adv Math 203:256–318, 2006), and ideas contained in previous works by Seeger (J Am Math Soc 9:95–105 1996) and Fan and Sato (Tohoku Math J 53:265–284, 2001).
publishDate 2019
dc.date.none.fl_str_mv 2019-07
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/11336/85550
Kangwei, Li; Pérez, Carlos; Rivera Ríos, Israel Pablo; Roncal, Luz; Weighted Norm Inequalities for Rough Singular Integral Operators; Springer; The Journal Of Geometric Analysis; 29; 3; 7-2019; 2526-2564
1050-6926
1559-002X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/85550
identifier_str_mv Kangwei, Li; Pérez, Carlos; Rivera Ríos, Israel Pablo; Roncal, Luz; Weighted Norm Inequalities for Rough Singular Integral Operators; Springer; The Journal Of Geometric Analysis; 29; 3; 7-2019; 2526-2564
1050-6926
1559-002X
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%2Fs12220-018-0085-4
info:eu-repo/semantics/altIdentifier/doi/10.1007/s12220-018-0085-4
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1701.05170
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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