Sharp weighted estimates for the multilinear maximal operator

Abstract

The paper contains the study of the weighted $L^{p_1}\times L^{p_2}\times \dots \times L^{p_m}\to L^p$ 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 for weights satisfying the multilinear Muckenhoupt condition.

arXiv comment27 pages, 2 figures