Hausdorff Operators on Weighted Mixed Norm Fock Spaces

• DOI: 10.1007/s40840-025-01832-6
• Publication Date: 2025-02-06T10:31:55Z
• Authors: Yongqing Liu
• Keywords: Mathematics - Functional Analysis; 30H20, 47G10, 47A35; FOS: Mathematics; Functional Analysis (math.FA)

In this paper, we study Hausdorff operator $\mathcal{H}_μ$ on a large class of weighted mixed norm Fock spaces $F_ϕ^{p,q}$ for $1\leq p,q\leq\infty$. The boundedness and compactness of $\mathcal{H}_μ$ on $F_ϕ^{p,q}$ are characterized. As applications, we give when Hausdorff operator on $F_ϕ^{p,q}$ is power bounded or uniformly mean ergodic.<br/>17 pages<br/>