Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures

As shown in Aldaz (Bull. Lond. Math. Soc. 39:203-208, 2007), the lowest constants appearing in the weak type (1, 1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here we extend this r...

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Detalles Bibliográficos
Autores: Aldaz, J.M. [0000-0001-8472-2606], Lazaro, J.P. [0000-0001-5354-8940]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc6913b750603269e814b8
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc6913b750603269e814b8
Access Level:acceso abierto
Palabra clave:Maximal operators
Radial measures
Weak type bounds
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spelling Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measuresAldaz, J.M. [0000-0001-8472-2606]Lazaro, J.P. [0000-0001-5354-8940]Maximal operatorsRadial measuresWeak type boundsAs shown in Aldaz (Bull. Lond. Math. Soc. 39:203-208, 2007), the lowest constants appearing in the weak type (1, 1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here we extend this result to a wider class of radial measures and to some values of p > 1. Furthermore, we improve the previously known bounds for p = 1. Roughly speaking, whenever p ∈(1,1.03], if μ is defined by a radial, radially decreasing density satisfying some mild growth conditions, then the best constants c p,d,μ in the weak type (p, p) inequalities satisfy c p,d,μ ≥ 1.005 d for all d sufficiently large. We also show that exponential increase of the best constants occurs for certain families of doubling measures, and for arbitrarily high values of p. © 2010 Birkhäuser / Springer Basel AG.2010info:eu-repo/semantics/articleSubtype: Articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://investigacion.unirioja.es/documentos/5bbc6913b750603269e814b8reponame:RIUR. Repositorio Institucional de la Universidad de La Riojainstname:Universidad de La Rioja (UR)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1007/S11117-010-0051-2info:eu-repo/semantics/altIdentifier/wos/WOS:000291060100003info:eu-repo/semantics/altIdentifier/pissn/1385-1292Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures, 2010, vol. 15, núm. 2, pág. 199-213info:eu-repo/semantics/openAccessoai:portal.dialnet.es:doc/5bbc6913b750603269e814b82026-06-14T12:47:17Z
dc.title.none.fl_str_mv Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
title Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
spellingShingle Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
Aldaz, J.M. [0000-0001-8472-2606]
Maximal operators
Radial measures
Weak type bounds
title_short Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
title_full Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
title_fullStr Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
title_full_unstemmed Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
title_sort Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures
dc.creator.none.fl_str_mv Aldaz, J.M. [0000-0001-8472-2606]
Lazaro, J.P. [0000-0001-5354-8940]
author Aldaz, J.M. [0000-0001-8472-2606]
author_facet Aldaz, J.M. [0000-0001-8472-2606]
Lazaro, J.P. [0000-0001-5354-8940]
author_role author
author2 Lazaro, J.P. [0000-0001-5354-8940]
author2_role author
dc.subject.none.fl_str_mv Maximal operators
Radial measures
Weak type bounds
topic Maximal operators
Radial measures
Weak type bounds
description As shown in Aldaz (Bull. Lond. Math. Soc. 39:203-208, 2007), the lowest constants appearing in the weak type (1, 1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here we extend this result to a wider class of radial measures and to some values of p > 1. Furthermore, we improve the previously known bounds for p = 1. Roughly speaking, whenever p ∈(1,1.03], if μ is defined by a radial, radially decreasing density satisfying some mild growth conditions, then the best constants c p,d,μ in the weak type (p, p) inequalities satisfy c p,d,μ ≥ 1.005 d for all d sufficiently large. We also show that exponential increase of the best constants occurs for certain families of doubling measures, and for arbitrarily high values of p. © 2010 Birkhäuser / Springer Basel AG.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
Subtype: Article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://investigacion.unirioja.es/documentos/5bbc6913b750603269e814b8
url https://investigacion.unirioja.es/documentos/5bbc6913b750603269e814b8
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/S11117-010-0051-2
info:eu-repo/semantics/altIdentifier/wos/WOS:000291060100003
info:eu-repo/semantics/altIdentifier/pissn/1385-1292
Behavior of weak type bounds for high dimensional maximal operators defined by certain radial measures, 2010, vol. 15, núm. 2, pág. 199-213
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:RIUR. Repositorio Institucional de la Universidad de La Rioja
instname:Universidad de La Rioja (UR)
instname_str Universidad de La Rioja (UR)
reponame_str RIUR. Repositorio Institucional de la Universidad de La Rioja
collection RIUR. Repositorio Institucional de la Universidad de La Rioja
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