Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators

Autores
Berra, Fabio Martín; Carena, Marilina; Pradolini, Gladis Guadalupe
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give a direct proof without taking into account the associated maximal operator. We use this result to prove an analogous inequality for higher-order commutators. For a given Young function φ we also consider singular integral operators T whose kernels satisfy a Lφ-Hörmander property, and we find sufficient conditions on φ such that a mixed weak estimate holds for T and also for its higher order commutators T m b . We also obtain a mixed estimation for a wide class of maximal operators associated to certain Young functions of LlogL type which are in intimate relation with the commutators. This last estimate involves an arbitrary weight u and a radial function v which is not even locally integrable.
Fil: Berra, Fabio Martín. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Carena, Marilina. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pradolini, Gladis Guadalupe. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
MUCKENHOUPT WEIGHTS
BMO
COMMUTATORS
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:11336/167892
Acceder
id CONICETDig_4cc5ddf16de2d9c99ce2e3870579b007
oai_identifier_str oai:ri.conicet.gov.ar:11336/167892
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operatorsBerra, Fabio MartínCarena, MarilinaPradolini, Gladis GuadalupeMUCKENHOUPT WEIGHTSBMOCOMMUTATORShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give a direct proof without taking into account the associated maximal operator. We use this result to prove an analogous inequality for higher-order commutators. For a given Young function φ we also consider singular integral operators T whose kernels satisfy a Lφ-Hörmander property, and we find sufficient conditions on φ such that a mixed weak estimate holds for T and also for its higher order commutators T m b . We also obtain a mixed estimation for a wide class of maximal operators associated to certain Young functions of LlogL type which are in intimate relation with the commutators. This last estimate involves an arbitrary weight u and a radial function v which is not even locally integrable.Fil: Berra, Fabio Martín. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Carena, Marilina. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pradolini, Gladis Guadalupe. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaMichigan Mathematical Journal2019-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/167892Berra, Fabio Martín; Carena, Marilina; Pradolini, Gladis Guadalupe; Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators; Michigan Mathematical Journal; Michigan Mathematical Journal; 68; 9-2019; 527-5640026-2285CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1704.04953info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.1704.04953info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:19:39Zoai:ri.conicet.gov.ar:11336/167892instacron: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:34982025-09-10 13:19:40.071CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
title Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
spellingShingle Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
Berra, Fabio Martín
MUCKENHOUPT WEIGHTS
BMO
COMMUTATORS
title_short Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
title_full Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
title_fullStr Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
title_full_unstemmed Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
title_sort Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
dc.creator.none.fl_str_mv Berra, Fabio Martín
Carena, Marilina
Pradolini, Gladis Guadalupe
author Berra, Fabio Martín
author_facet Berra, Fabio Martín
Carena, Marilina
Pradolini, Gladis Guadalupe
author_role author
author2 Carena, Marilina
Pradolini, Gladis Guadalupe
author2_role author
author
dc.subject.none.fl_str_mv MUCKENHOUPT WEIGHTS
BMO
COMMUTATORS
topic MUCKENHOUPT WEIGHTS
BMO
COMMUTATORS
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 study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give a direct proof without taking into account the associated maximal operator. We use this result to prove an analogous inequality for higher-order commutators. For a given Young function φ we also consider singular integral operators T whose kernels satisfy a Lφ-Hörmander property, and we find sufficient conditions on φ such that a mixed weak estimate holds for T and also for its higher order commutators T m b . We also obtain a mixed estimation for a wide class of maximal operators associated to certain Young functions of LlogL type which are in intimate relation with the commutators. This last estimate involves an arbitrary weight u and a radial function v which is not even locally integrable.
Fil: Berra, Fabio Martín. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Carena, Marilina. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pradolini, Gladis Guadalupe. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give a direct proof without taking into account the associated maximal operator. We use this result to prove an analogous inequality for higher-order commutators. For a given Young function φ we also consider singular integral operators T whose kernels satisfy a Lφ-Hörmander property, and we find sufficient conditions on φ such that a mixed weak estimate holds for T and also for its higher order commutators T m b . We also obtain a mixed estimation for a wide class of maximal operators associated to certain Young functions of LlogL type which are in intimate relation with the commutators. This last estimate involves an arbitrary weight u and a radial function v which is not even locally integrable.
publishDate 2019
dc.date.none.fl_str_mv 2019-09
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/11336/167892
Berra, Fabio Martín; Carena, Marilina; Pradolini, Gladis Guadalupe; Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators; Michigan Mathematical Journal; Michigan Mathematical Journal; 68; 9-2019; 527-564
0026-2285
CONICET Digital
CONICET
url http://hdl.handle.net/11336/167892
identifier_str_mv Berra, Fabio Martín; Carena, Marilina; Pradolini, Gladis Guadalupe; Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators; Michigan Mathematical Journal; Michigan Mathematical Journal; 68; 9-2019; 527-564
0026-2285
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/1704.04953
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.1704.04953
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 Michigan Mathematical Journal
publisher.none.fl_str_mv Michigan Mathematical Journal
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_ 1842981074350637056
score 12.48226

Publicaciones similares