Hausdorff operators on weighted mixed norm Fock spaces

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 $1\le p,q\le \mathrm{\infty }$. 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.