单位球的Bergman空间上Schatten类加权复合算子

摘要

本文研究了单位球的Bergman空间上Schatten类加权复合算子,得到了这种加权复合算子属于Schatten-Von Neumann理想Sp的几个充要条件.作为推论给出了W(ψ),ψ是一个Hilbert-Schmidt算子的充要条件是∫Bn |ψ(w)|2/(1-|(ψ)(w)|2)n+1 dV(w)＜∞.%We consider the Schatten class weighted composition operators on the Bergman space of the unit ball. The main result is several necessary and sufficient conditions for such kind of weighted composition operators belong to the Schatten-Von Neumann ideal Sp. As a corollary, we now have that W(ψ),ψ is a Hilbert-Schmidt operator if and only if ∫Bn |ψ(w)|2/(1-|(ψ)(w)|2)n+1 dV(w) ＜∞.