Weighted estimates for the multilinear maximal operator

Abstract The paper contains the study of weighted $$L^{p_1}\times L^{p_2}\times \ldots \times L^{p_m}\rightarrow L^p$$ L p 1 × 2 … m → estimates for multilinear maximal operator, in context abstract probability spaces equipped with a tree-like structure. Using Bellman function method, we identify associated optimal constants symmetric case $$p_1=p_2=\ldots =p_m$$ = , and tight constant remaining choices exponents.