New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory

A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to bu...

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Detalhes bibliográficos
Autores: Lerner, Andrei K., Ombrosi, Sheldy J., Pérez Moreno, Carlos, Torres, Rodolfo H., Trujillo González, Rodrigo Francisco
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/47293
Acesso em linha:http://hdl.handle.net/11441/47293
https://doi.org/10.1016/j.aim.2008.10.014
Access Level:acceso abierto
Palavra-chave:Multilinear singular integrals
Calderón-Zygmund theory
Maximal operators
Weighted norm inequalities
Commutators
Descrição
Resumo:A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calder´on-Zygmund operators with BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators.