Weighted Morrey-Herz space estimates for rough Hausdorff operator and its commutators

TL;DR

This paper investigates the boundedness of rough Hausdorff operators and their commutators on Herz, Morrey, and Morrey-Herz spaces with homogeneous weights, providing necessary and sufficient conditions and operator norm estimates.

Contribution

It introduces new boundedness criteria and norm estimates for rough Hausdorff operators and their commutators on these function spaces, with symbols in Lipschitz space.

Findings

Established necessary and sufficient conditions for boundedness.

Derived explicit operator norm estimates.

Proved boundedness of commutators with Lipschitz symbols.

Abstract

In this paper, we give necessary and sufficient conditions for the boundedness of rough Hausdorff operators on Herz, Morrey and Morrey-Herz spaces with absolutely homogeneous weights. Especially, the estimates for operator norms in each case are worked out. Moreover, we also establish the boundedness of the commutators of rough Hausdorff operators on the such spaces with their symbols belonging to Lipschitz space.