Weighted estimates for the multilinear maximal operator

The paper contains the study of the weighted L-p1 x L-p2 x ... x L-pm -> L-p estimates for the multilinear maximal operator, in the context of abstract probability spaces equipped with a tree-like structure. Using the Bellman function method, we identify the associated optimal constants in the symmetric case p(1) = p(2) = ... = p(m) , and a tight constant for remaining choices of exponents.