摘要
给定单位圆盘D上的全纯自映射和g∈H(D),定义复合积分算子Tg,φf(z)=∫0zf(φ(t))g′(t)dt,利用复变函数和泛函分析的知识,通过构造试验函数的方法,刻画了H∞空间到混合模空间复合积分算子的有界性和紧性,得到了在相应空间上该算子为有界算子和紧算子的充要条件.
Given φ：D → D a holomorphic mapping,g∈ H（D）,we define the composition integral operators Tg,φf（z）=∫z0f（φ（t））g′（t）dt.By using the knowledge of complex analysis and functional analysis,we characterize the boundedness and compactness of Tg,φ from H∞ space to the mixed-norm space by the tested functions.
出处
《湖州师范学院学报》
2010年第1期40-42,47,共4页
Journal of Huzhou University
基金
National Natural Science Foundation of China(10771064)
Natural Science Foundation of Zhejiang Province(Y7080197,Y6090036)
Characteristic Subject of China"Mathematics and applied mathematics",Delicate Course of China"theory of functions of a complex variable",Educational Innovation of Zhejiang province(yb07109)
Foundation of Creative Group in Colleges and Universities of Zhejiang Province(T200924)
关键词
复合积分算子
H∞空间
混合模空间
有界性
紧性
Composition integral operator
H∞ space
Mixed-norm space
Boundedness
Compactness
