Hausdorff operators on weighted mixed norm Fock spaces

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.