The Multilinear Spherical Maximal Function in one dimension

Abstract

In dimension $n=1$ we obtain $L^{p_1}(\mathbb{R})\times \cdots \times L^{p_m}(\mathbb{R})$ to $L^p(\mathbb{R})$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples that indicate the optimality of our results.