Hypercyclicity of weighted shifts on weighted Bergman spaces

Abstract

We study the continuity, and dynamical properties (hypercyclicity, periodic vectors, and chaos) for a weighted backward shift $B_w$ on a weighted Bergman space $A_{\varphi }^p$ based on the norm estimates of coefficient functionals on $A_{\varphi }^p$. Here, the weight function $\varphi (z)$ is mostly radial, but our work will also involve a (non-radial) subharmonic weight. We provide a complete characterization of hypercyclic shifts $B_w$ on $A_{\varphi }^p$ when $\varphi$ is an (integrable) radial weight. The coefficient multipliers obtained in this paper for certain weights are new.

19 pages