The paper contains the study of the weighted \(L^{p_1}\times L^{p_2}\times \ldots \times L^{p_m}\rightarrow L^p\) 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 \(p_1=p_2=\ldots =p_m\), and a tight constant for remaining choices of exponents.

中文翻译：

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多重线性最大算子的加权估计

该论文包含对多重线性最大算子的加权\(L^{p_1}\times L^{p_2}\times \ldots \times L^{p_m}\rightarrow L^p\)估计的研究，在上下文中具有树状结构的抽象概率空间。使用 Bellman 函数方法，我们确定了对称情况下的相关最优常数\(p_1=p_2=\ldots =p_m\)，以及剩余指数选择的紧常数。