AI 中文总结
该研究给出加权福克空间上加权复合算子有界、紧和希尔伯特-施密特类的刻画及本质范数估计，方法依赖米塔格-莱夫勒函数渐近行为，还建立指数权重加权复合算子准则并恢复复合算子相应结果。
AI 中文摘要
我们给出了作用于加权福克空间上有界、紧和希尔伯特-施密特类加权复合算子的完整刻画，扩展了Le[11]给出的经典福克空间刻画。还给出了这些算子本质范数的一个估计。我们的方法依赖于米塔格-莱夫勒函数的渐近行为。作为应用，我们建立了指数权重加权复合算子的显式准则，并恢复了复合算子的相应结果。
英文摘要
We provide a complete characterization of the bounded, compact, and Hilbert-Schmidt class weighted composition operators acting on weighted Fock spaces, extending the classical Fock space characterization due to Le [11]. An estimate for the essential norm of these operators is also provided. Our approach relies on the asymptotic behavior of the Mittag-Leffler function. As applications, we establish explicit criteria for weighted composition operators with exponential weights and recover corresponding results for composition operators.
