B~α到Z~β空间广义复合算子的新刻画（英文）

A New Characterization of Generalized Composition Operators from B~α Spaces into Z~β Spaces

令D为一维复平面上的单位圆盘,φ是定义在D上的解析自映射,g是定义在D上的解析函数.通过一种新的方式刻画了C^gφ:Bα→Zβ的有界性和紧性.此外还给出了C^gφ:Bα→Zβ本性范数的估计.

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 C^gφ:B^α →Z^β in a new way. Moreover, the estimate for the essential norm of the generalized composition operator C^gφ:B^α →Z^β is also investigated.