加权复合算子作用在B_∞(∏^+)的有界性和紧性

Boundedness and compactness of weighted composition operator on Bloch spaces of upper half-plane

目的研究了加权复合算子作用在B∞(∏+)有界性和紧性。方法采用了泛函分析和复分析的方法。结果得到了加权复合算子是有界算子或紧算子的充要条件。结论上半平面上得到的结果与在圆盘上的结果不同。

Aim To discuss the boundedness and compactness of weighted composition operator on Bloch spaces of upper half-plane. Methods The method of functional analysis and complex analysis is adopted. Results The necessary and sufficient conditions, under which the weighted composition operator is a bounded or compact operator, are obtained. Conclusion The results on the upper half-plane are different from those on the open unit disk.