Sharp Bound for the Generalized $m$-Linear $n$-Dimensional Hardy-Littlewood-Pόlya Operator

Abstract

In this paper, we calculate the sharp bound for the generalized $m$-linear $n$-dimensional Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Pόlya operator on power weighted central and noncentral homogeneous Morrey spaces is obtained. Finally, we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces, which generalizes the previous results.