# Two Weighted estimates for multilinear Hausdorff Operators on the Morrey-Herz Spaces

## TL;DR

This paper investigates the boundedness of multilinear Hausdorff operators on weighted Morrey, Herz, and Morrey-Herz spaces, providing necessary and sufficient conditions, especially with Muckenhoupt weights.

## Contribution

It introduces new boundedness criteria for multilinear Hausdorff operators on these weighted function spaces, extending previous results.

## Key findings

- Established necessary and sufficient conditions for boundedness.
- Provided sufficient conditions with respect to Muckenhoupt weights.
- Extended the theory to a broader class of weighted spaces.

## Abstract

The purpose of this paper is to establish some neccessary and sufficient conditions for the boundedness of a general class of multilinear Hausdorff operators that acts on the product of some two weighted function spaces such as the two weighted Morrey, Herz and Morrey-Herz spaces. Moreover, some sufficient conditions for the boundedness of multilinear Hausdorff operators on the such spaces with respect to the Muckenhoupt weights are also given.