Hypercyclicity of Weighted shifts on weighted Bergman and Dirichlet spaces

Abstract: Let $B_w$ and $F_w$ denote, respectively, the weighted backward and forward shift operators defined on the weighted Bergman space $A^p_{\phi}$, or the weighted Dirichlet space ${D}^p_{\phi}$ of the unit disc, where the weight function $\phi(z)$ is mostly radial. We first obtain sufficient conditions for $B_w$ and $F_w$ to be continuous on these spaces. For radial weights, we derive norm estimates for coefficient functionals on $A^p_{\phi}$ and $D^p_{\phi}$, and using those estimates we infer when the weighted shifts or their adjoints are hypercyclic. We also deal with a non-radial case.