多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子

Weighted composition operators from weighted Bergman space to Bloch-type spaces on the polydisc

设Dn是Cn中的单位多圆柱,φ(z)=(φ1(z),φ2(z),…,φn(z))是Dn的一个全纯自映射,ψ(z)是Dn上的全纯函数.研究了单位多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子ψCφ;通过φ和ψ的函数特征,分别给出了单位多圆柱上从加权Bergman空间到Bloch型空间的加权复合算子ψCφ的有界性和紧性的充分必要条件.

Let φ（z）=（φ1（z）,φ2（z）,…,φn（z））be a holomorphic self-map of Dn and ψ（z）a holomorphic function on Dn ,where Dn is the unit polydisc of Cn . It was investigated the weighted composition operator ψCφfrom weighted Bergman space to the Bloch-type spaces on the unit polydisc. In terms of the function property of φ and ψ,the sufficient and necessary conditions were given for the weighted composition operator ψCφ to be bounded and compact from weighted Bergman space to the Bloch-type spaces.