%0 Journal Article
%A Lerner, Andrei
%A Ombrosi, Sheldy Javier
%A Pérez, Carlos
%A Torres, Rodolfo
%A Trujillo González, Rodrigo
%T New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory
%D 2009
%@ 0001-8708
%U https://hdl.handle.net/20.500.14352/97591
%X 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.
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