单位球上Dirichlet型空间D_q到Zygmund型空间Z^p的加权Cesaro算子

Extended Cesaro operators from Dirichlet type space D_q to Zygmund type space Z^p in the unit ball

利用泛函分析多复变的方法,研究了单位球上Dirichlet型空间到Zygmund型空间的加权Cesaro算子的有界性和紧性问题.获得了单位球上Dirichlet型空间到Zygmund型空间的加权Cesaro算子为有界算子和紧算子的充要条件.

Some questions of Extended Cesaro operators from Dirichlet type space to Zygmund type space in the unit ball are studied in this paper.By the methods of functional analysis and several complex variables,the necessary and sufficient conditions are given for Extended Cesaro operators to be bounded and compact from Dirichlet type space to Zygmund type space in the unit ball.