Boundedness and compactness for commutators of singular integrals related to a critical radius function

Autores
Bongioanni, Bruno; Harboure, Eleonor Ofelia; Quijano, Pablo
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We work in the general framework of a family of singular integrals with kernels controlled in terms of a critical radius function ρ. This family models the harmonic analysis derived from the Schr¨odinger operator L = −∆ + V , where the non-negative potential V satisfies an appropriate reverse H¨older condition. For their commutators, we find sufficient conditions on the symbols for boundedness and/or compactness when acting on weighted Lp spaces. In all cases, the classes of symbols and weights are larger than their classical counterparts, BMO, CMO and Ap. When these general results are applied to the Schr¨odinger context, we obtain boundedness and compactness for commutators of operators like ∇L−1/2 , ∇2L−1 , V 1/2L−1/2 , V 1/2∇L−1 , V L−1 and Liα. As in Uchiyama’s classical paper, we give a full description of the class for compactness, CMO∞ρ , assuming ρ to be bounded. Finally, we provide examples showing that CMO is strictly contained in CMO∞ρ for any ρ, bounded or not.
Fil: Bongioanni, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Quijano, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
Boundedness
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:11336/213464
Acceder
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spelling Boundedness and compactness for commutators of singular integrals related to a critical radius functionBongioanni, BrunoHarboure, Eleonor OfeliaQuijano, PabloBoundednesshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We work in the general framework of a family of singular integrals with kernels controlled in terms of a critical radius function ρ. This family models the harmonic analysis derived from the Schr¨odinger operator L = −∆ + V , where the non-negative potential V satisfies an appropriate reverse H¨older condition. For their commutators, we find sufficient conditions on the symbols for boundedness and/or compactness when acting on weighted Lp spaces. In all cases, the classes of symbols and weights are larger than their classical counterparts, BMO, CMO and Ap. When these general results are applied to the Schr¨odinger context, we obtain boundedness and compactness for commutators of operators like ∇L−1/2 , ∇2L−1 , V 1/2L−1/2 , V 1/2∇L−1 , V L−1 and Liα. As in Uchiyama’s classical paper, we give a full description of the class for compactness, CMO∞ρ , assuming ρ to be bounded. Finally, we provide examples showing that CMO is strictly contained in CMO∞ρ for any ρ, bounded or not.Fil: Bongioanni, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Quijano, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaConsejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral2021-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/213464Bongioanni, Bruno; Harboure, Eleonor Ofelia; Quijano, Pablo; Boundedness and compactness for commutators of singular integrals related to a critical radius function; Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral; IMAL Preprints; 52; 3-2021; 1-282451-7100CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://imal.conicet.gov.ar/wp-content/uploads/sites/151/2021/07/2021-0052.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:20:45Zoai:ri.conicet.gov.ar:11336/213464instacron: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 13:20:46.069CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Boundedness and compactness for commutators of singular integrals related to a critical radius function
title Boundedness and compactness for commutators of singular integrals related to a critical radius function
spellingShingle Boundedness and compactness for commutators of singular integrals related to a critical radius function
Bongioanni, Bruno
Boundedness
title_short Boundedness and compactness for commutators of singular integrals related to a critical radius function
title_full Boundedness and compactness for commutators of singular integrals related to a critical radius function
title_fullStr Boundedness and compactness for commutators of singular integrals related to a critical radius function
title_full_unstemmed Boundedness and compactness for commutators of singular integrals related to a critical radius function
title_sort Boundedness and compactness for commutators of singular integrals related to a critical radius function
dc.creator.none.fl_str_mv Bongioanni, Bruno
Harboure, Eleonor Ofelia
Quijano, Pablo
author Bongioanni, Bruno
author_facet Bongioanni, Bruno
Harboure, Eleonor Ofelia
Quijano, Pablo
author_role author
author2 Harboure, Eleonor Ofelia
Quijano, Pablo
author2_role author
author
dc.subject.none.fl_str_mv Boundedness
topic Boundedness
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 work in the general framework of a family of singular integrals with kernels controlled in terms of a critical radius function ρ. This family models the harmonic analysis derived from the Schr¨odinger operator L = −∆ + V , where the non-negative potential V satisfies an appropriate reverse H¨older condition. For their commutators, we find sufficient conditions on the symbols for boundedness and/or compactness when acting on weighted Lp spaces. In all cases, the classes of symbols and weights are larger than their classical counterparts, BMO, CMO and Ap. When these general results are applied to the Schr¨odinger context, we obtain boundedness and compactness for commutators of operators like ∇L−1/2 , ∇2L−1 , V 1/2L−1/2 , V 1/2∇L−1 , V L−1 and Liα. As in Uchiyama’s classical paper, we give a full description of the class for compactness, CMO∞ρ , assuming ρ to be bounded. Finally, we provide examples showing that CMO is strictly contained in CMO∞ρ for any ρ, bounded or not.
Fil: Bongioanni, Bruno. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Quijano, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description We work in the general framework of a family of singular integrals with kernels controlled in terms of a critical radius function ρ. This family models the harmonic analysis derived from the Schr¨odinger operator L = −∆ + V , where the non-negative potential V satisfies an appropriate reverse H¨older condition. For their commutators, we find sufficient conditions on the symbols for boundedness and/or compactness when acting on weighted Lp spaces. In all cases, the classes of symbols and weights are larger than their classical counterparts, BMO, CMO and Ap. When these general results are applied to the Schr¨odinger context, we obtain boundedness and compactness for commutators of operators like ∇L−1/2 , ∇2L−1 , V 1/2L−1/2 , V 1/2∇L−1 , V L−1 and Liα. As in Uchiyama’s classical paper, we give a full description of the class for compactness, CMO∞ρ , assuming ρ to be bounded. Finally, we provide examples showing that CMO is strictly contained in CMO∞ρ for any ρ, bounded or not.
publishDate 2021
dc.date.none.fl_str_mv 2021-03
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/11336/213464
Bongioanni, Bruno; Harboure, Eleonor Ofelia; Quijano, Pablo; Boundedness and compactness for commutators of singular integrals related to a critical radius function; Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral; IMAL Preprints; 52; 3-2021; 1-28
2451-7100
CONICET Digital
CONICET
url http://hdl.handle.net/11336/213464
identifier_str_mv Bongioanni, Bruno; Harboure, Eleonor Ofelia; Quijano, Pablo; Boundedness and compactness for commutators of singular integrals related to a critical radius function; Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral; IMAL Preprints; 52; 3-2021; 1-28
2451-7100
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://imal.conicet.gov.ar/wp-content/uploads/sites/151/2021/07/2021-0052.pdf
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 Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral
publisher.none.fl_str_mv Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Matemática Aplicada del Litoral
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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