Sharp Bound for the Generalized m-Linear n-Dimensional Hardy-Littlewood-Po?lya Operator

In this paper, we calculate the sharp bound for the generalized m-linear n -dimensional Hardy-Littlewood-Polya operator on power weighted central and non -central homogeneous Morrey spaces. As an application, the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous 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.

Automated summary

In this paper, we compute the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces. An application of this is obtaining the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces. Finally, the sharp bound for the Hausdorff operator on power weighted central and non-central homogeneous Morrey spaces is also found, generalizing previous results.