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...
| Autores: | , |
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| 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 |
| 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. |
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