Regularity of the Hardy-Littlewood maximal operator on block decreasing functions

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving th...

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Detalhes bibliográficos
Autores: Aldaz, J.M. [0000-0001-8472-2606], Lázaro, F.J.P. [0000-0001-5354-8940]
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:España
Recursos:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc699eb750603269e81e7a
Acesso em linha:https://investigacion.unirioja.es/documentos/5bbc699eb750603269e81e7a
Access Level:acceso abierto
Palavra-chave:Functions of bounded variation
Maximal function
Descrição
Resumo:We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the l∞-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special. © Instytut Matematyczny PAN, 2009.