加权Bergman空间上复合算子的积

Products of Several Composition Operators on Weighted Bergman Spaces

设A2,α(D)表示L2,α(D)中解析函数的全体构成的闭子空间,研究A2,α(D)上复合算子的积,得到了CψC*φ紧的一个必要条件和C*φCψ紧的一个充分条件.

Let A^2a（D） denote the closed subspace of L^2a（D） consisting of analytic functions in the unit disk D. The compactness of the products of composition operator is studied. The main results are a necessary condition that CφCφ, is a compact operator on A^2a （D） and a sufficient condition that CφCφ is a compact operator on A^2a（D）.