Multilinear Cesàro maximal operators

The study of the almost everywhere convergence of the product of m Cesàro- α averages leads to the characterization of the boundedness of the associated multi(sub)linear maximal operator. We characterize weighted weak type and strong type inequalities for this operator, extending results by Lerner et al. [A. Lerner, S. Ombrosi, C. Pérez, R. Torres, R. Trujillo-González, New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory, Adv. Math. 220 (2009) 1222–1264.]. We also study the restricted weak type inequalities which are of particular interest in our case (they were not considered by Lerner et al.).