Weighted estimates for the multilinear maximal operator

The paper contains the study of the weighted $$L^{p_1}\times L^{p_2}\times \ldots \times L^{p_m}\rightarrow L^p$$ L p 1 × L p 2 × … × L p m → 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 $$p_1=p_2=\ldots =p_m$$ p 1 = p 2 = … = p m , and a tight constant for remaining choices of exponents.