Hausdorff operators on weighted mixed norm Fock spaces

TL;DR

This paper investigates the properties of Hausdorff operators on weighted mixed norm Fock spaces, providing characterizations of their boundedness, compactness, and ergodic behavior.

Contribution

It offers new criteria for the boundedness and compactness of Hausdorff operators on these complex function spaces.

Findings

Characterization of boundedness of $\

Criteria for compactness of $\

Conditions for power boundedness and mean ergodicity

Abstract

In this paper, we study Hausdorff operator $\mathcal{H}_\mu$ on a large class of weighted mixed norm Fock spaces $F_\phi^{p,q}$ for $1\leq p,q\leq\infty$. The boundedness and compactness of $\mathcal{H}_\mu$ on $F_\phi^{p,q}$ are characterized. As applications, we give when Hausdorff operator on $F_\phi^{p,q}$ is power bounded or uniformly mean ergodic.