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...

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Detalhes bibliográficos
Autores: Lerner, Andrei K., Ombrosi, Sheldy
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
Descrição
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.