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 than 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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Bibliographic Details
Authors: Lerner, Andrei K., Ombrosi, Sheldy Javier, Pérez, Carlos, Torres, Rodolfo, Trujillo Gonzalez, Rodrigo
Format: article
Status:Published version
Publication Date:2009
Country:Argentina
Institution:Consejo Nacional de Investigaciones Científicas y Técnicas
Repository:CONICET Digital (CONICET)
Language:English
OAI Identifier:oai:ri.conicet.gov.ar:11336/79548
Online Access:http://hdl.handle.net/11336/79548
Access Level:Open access
Keyword:CalderÓN-Zygmund Theory
Commutators
Maximal Operators
Multilinear Singular Integrals
Weighted Norm Inequalities
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Description
Summary:A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than 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 Calderón-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.