Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree

Autores
Ombrosi, Sheldy Javier; Rivera Ríos, Israel Pablo; Safe, Martin Dario
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if s=1⁠. Some examples of nontrivial weights such that the weighted weak type (1,1) estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established.
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: 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
Fil: Safe, Martin Dario. 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
WEIGHTS
MAXIMAL
FEFFERMAN-STEIN
TREES
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:11336/129310
Acceder
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spelling Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary TreeOmbrosi, Sheldy JavierRivera Ríos, Israel PabloSafe, Martin DarioWEIGHTSMAXIMALFEFFERMAN-STEINTREEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if s=1⁠. Some examples of nontrivial weights such that the weighted weak type (1,1) estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established.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; ArgentinaFil: 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; ArgentinaFil: Safe, Martin Dario. 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; ArgentinaOxford University Press2020-08-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129310Ombrosi, Sheldy Javier; Rivera Ríos, Israel Pablo; Safe, Martin Dario; Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree; Oxford University Press; International Mathematics Research Notices; 2021; 4; 27-8-2020; 2736-27621073-7928CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnaa220/5897128info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnaa220info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2003.10034info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:01Zoai:ri.conicet.gov.ar:11336/129310instacron: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 09:48:02.248CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
title Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
spellingShingle Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
Ombrosi, Sheldy Javier
WEIGHTS
MAXIMAL
FEFFERMAN-STEIN
TREES
title_short Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
title_full Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
title_fullStr Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
title_full_unstemmed Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
title_sort Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
dc.creator.none.fl_str_mv Ombrosi, Sheldy Javier
Rivera Ríos, Israel Pablo
Safe, Martin Dario
author Ombrosi, Sheldy Javier
author_facet Ombrosi, Sheldy Javier
Rivera Ríos, Israel Pablo
Safe, Martin Dario
author_role author
author2 Rivera Ríos, Israel Pablo
Safe, Martin Dario
author2_role author
author
dc.subject.none.fl_str_mv WEIGHTS
MAXIMAL
FEFFERMAN-STEIN
TREES
topic WEIGHTS
MAXIMAL
FEFFERMAN-STEIN
TREES
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, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if s=1⁠. Some examples of nontrivial weights such that the weighted weak type (1,1) estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established.
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: 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
Fil: Safe, Martin Dario. 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, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if s=1⁠. Some examples of nontrivial weights such that the weighted weak type (1,1) estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established.
publishDate 2020
dc.date.none.fl_str_mv 2020-08-27
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/11336/129310
Ombrosi, Sheldy Javier; Rivera Ríos, Israel Pablo; Safe, Martin Dario; Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree; Oxford University Press; International Mathematics Research Notices; 2021; 4; 27-8-2020; 2736-2762
1073-7928
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129310
identifier_str_mv Ombrosi, Sheldy Javier; Rivera Ríos, Israel Pablo; Safe, Martin Dario; Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree; Oxford University Press; International Mathematics Research Notices; 2021; 4; 27-8-2020; 2736-2762
1073-7928
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://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnaa220/5897128
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnaa220
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2003.10034
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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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