A boundedness criterion for general maximal operators
We consider maximal operators Mβ with respect to a basis β. In the case when Mβ satisfies a reversed weak type inequality, we obtain a boundedness criterion for Mβ on an arbitrary quasiBanach function space X. Being applied to specific β X this criterion yields new and short proofs of a number of we...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:52294 |
| Acesso em linha: | https://ddd.uab.cat/record/52294 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_54110_03 |
| Access Level: | acceso abierto |
| Palavra-chave: | Maximal operators One-sided maximal function |
| Resumo: | We consider maximal operators Mβ with respect to a basis β. In the case when Mβ satisfies a reversed weak type inequality, we obtain a boundedness criterion for Mβ on an arbitrary quasiBanach function space X. Being applied to specific β X this criterion yields new and short proofs of a number of well-known results. Our principal application is related to an open problem on the boundedness of the two-dimensional one-sided maximal function M+ Lp/w. |
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