中文摘要：

设X是可分的Hilbert空间,并设φ和ψ是单位球到自身的线性分式变换.本文研究了多变量向量值Bergman空间B1（X）的基本性质,利用泛函分析与复分析的方法,刻画了B1（X）上的乘积算子CφC＊ψ和C＊ψCφ的弱紧性,把一维的弱紧性结论推广到了多维.

英文摘要：

Let Xbe a separable Hilbert space,andφ,ψbe linear fractional self-maps on unit ball.In this paper,we study the basic properties of the vector-valued Bergman space B1（X）.By the method of functional analysis and complex analysis,we consider the weak compactness of product operators CφCψ~＊and Cψ~＊Cφon B1（X）.This generalizes the results of one-dimension into multi-dimension.