The multilinear strong maximal function

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted...

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Detalles Bibliográficos
Autores: Grafakos, Loukas, Liu, Liguang, Pérez Moreno, Carlos, Torres, Rodolfo H.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2011
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42364
Acceso en línea:http://hdl.handle.net/11441/42364
https://doi.org/10.1007/s12220-010-9174-8
Access Level:acceso abierto
Palabra clave:Maximal operators
weighted norm inequalities
multilinear singular integrals
Calder´on-Zygmund theory
commutators
Descripción
Sumario:A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear maximal functions associated with bases of open sets are studied too. Bilinear interpolation results between distributional estimates, such as those satisfied by the multivariable strong maximal function, are also proved.