摘要： Let φ be analytic self-map of the open unit disk D in the complex plane C and g be an analytic function on D . In this paper, we characterize the boundedness and compactness of the generalized composition operator Cgφ:Bα→Zβin a new way. Moreover, the estimate for the essential norm of the generalized composition operatorCgφ:Bα→Zβis also investigated.