Hypercyclic Composition Operators]{Hypercyclic composition operators on the little Bloch space $\mathcal{B}_0$ and the Besov spaces $B_p

Abstract

Let $S(\mathbb{D})$ be the collection of all holomorphic self-maps on $\mathbb{D}$ of the complex plane $\mathbb{C}$, and $C_{\varphi}$ the composition operator induced by $\varphi\in S(\mathbb{D})$. We obtain that there are no hypercyclic composition operators on the little Bloch space $\mathcal{B}_0$ and the Besov space $B_p$.