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 ...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).展开更多
基金partially supported by the National Natural Science Foundation(Grant No.12171373)of Chinasupported by the Fundamental Research Funds for the Central Universities(Grant No.GK202207018)of China。
文摘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).
