Weighted estimates for the multilinear maximal function

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 \mathcal{M} introduced in Lerner et al. A multilinear version of the B_p theorem from Hyt\"onen and P\'erez is also obtained and a mixed A_{\vec{P}}-W_{\vec{P}}^{\infty} bound for \mathcal{M} is proved as well.