Weighted estimates for the multilinear maximal operator

Abstract

The paper contains the study of the weighted Lp1×Lp2×…×Lpm→Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^{p_1}\ imes L^{p_2}\ imes \\ldots \ imes L^{p_m}\\rightarrow L^p$$\\end{document} 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 p1=p2=…=pm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_1=p_2=\\ldots =p_m$$\\end{document}, and a tight constant for remaining choices of exponents.