在一般加权Bergman空间上的广义Volterra型算子

Generalized Volterra Type Operators on General Weighted Bergman Space

Bergman空间上的算子理论是函数空间与算子理论的重要内容。利用Volterra算子、加权复合算子、微分算子之间的关系,用一种全新的方法简捷地刻画了一般加权Bergman空间上广义Volterra算子的有界性和紧性,拓展了相关的结论。文中的方法极大地简化了经典的证明,对相关算子的研究有一定的启发。

Operator theory on Bergman spaces is an important part of the theory on function spaces.Using the relations among Volterra operators,weighted composition operators and differential operators,the boundedness and compactness of generalized Volterra operators between Bergman spaces induced regular weights are characterized in a new and much easier way.The method used here simplifies the classical proof and directs a new way to deal with the similar questions.