Integration Operators on Spaces of Dirichlet Series  

作　　者：Jia Le CHEN Mao Fa WANG 

机构地区：[1]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,P.R.China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第10期1919-1938,共20页数学学报（英文版）

基　　金：partially supported by the National Natural Science Foundation(Grant No.12171373)of China;supported by the Fundamental Research Funds for the Central Universities(Grant No.GK202207018)of China。

摘　　要：We first study the Volterra operator V acting on spaces of Dirichlet series.We prove that V is bounded on the Hardy space H_(0)^(p)for any 0<p≤∞,and is compact on H_(0)^(p)for 1<p≤∞.Furthermore,we show that V is cyclic but not supercyclic on H_(0)^(p)for any 0<p<∞.Corresponding results are also given for V acting on Bergman spaces H_(w,0)^(p).We then study the Volterra type integration operators T_(g).We prove that if T_(g)is bounded on the Hardy space H_(p),then it is bounded on the Bergman space H_(w)^(p).

关 键 词：Integration operator Dirichlet series Hardy space Bergman space 

分 类 号：O177[理学—数学]