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Hausdorff operators on weighted mixed norm Fock spaces (2410.07748v1)
Published 10 Oct 2024 in math.FA
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.