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

Andrei K. Lerner, Sheldy J. Ombrosi , Carlos Pérez Moreno , Rodolfo H. Torres, Rodrigo Trujillo González

• 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