Two-weighted inequalities for Hausdorff operators in Herz-type Hardy spaces

TL;DR

This paper establishes the boundedness of matrix and rough Hausdorff operators in two weighted Herz-type Hardy spaces, generalizing previous results by leveraging atomic decomposition techniques and weight class properties.

Contribution

It introduces new boundedness results for Hausdorff operators in Herz-type Hardy spaces with power and Muckenhoupt weights, extending prior work in the field.

Findings

Boundedness of matrix Hausdorff operators proved

Boundedness of rough Hausdorff operators established

Generalization of previous results by Chen et al. and Ruan, Fan

Abstract

In this paper, we prove the boundedness of matrix Hausdorff operators and rough Hausdorff operators in the two weighted Herz-type Hardy spaces associated with both power weights and Muckenhoupt weights. By applying the fact that the standard infinite atomic decomposition norm on two weighted Herz-type Hardy spaces is equivalent to the finite atomic norm on some dense subspaces of them, we generalize some previous known results due to Chen et al. [7] and Ruan, Fan [34].