中文摘要：

研究了加权Hardy空间H^2（β）上复合算子Cφ的紧性问题．给出了当φ满足Rudin正交条件时Cφ是紧算子的充要条件．同时，提供了一种关于复合算子Cφ本质范数｜｜Cφ｜｜的新刻画．

英文摘要：

In this paper,we study the compactness of composition operator Cφ on the weighted Hardy space H2 （/？） ,concluding that symbol φ satisfies the Rudin＇s orthogonality condition is the necessary and sufficient conditions of composition operator Cφ being compact. Moreover, we provide a new characterization for the essential norm of the composition operator Cφ .