Weighted estimates for the multilinear maximal function

Abstract

A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows to obtain a multilinear analogue of Sawyer’s two weight theorem for the multisublinear maximal function M introduced in [8] A.K. Lerner, S. Ombrosi, C. Pérez, R.H. Torres and R. Trujillo-González, New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory, Advances in Math. 220, 1222–1264 (2009). A multilinear version of the Bp theorem from [6] T. Hytönen and C. Pérez, Sharp weighted bounds involving A∞, Analysis & PDE, (to appear) is also obtained and a mixed AP~ − W ∞ P~ bound for M is proved as well.