Mean Ergodicity of Multiplication Operators on the Bloch and Besov Spaces

In this paper, the power boundedness and mean ergodicity of multiplication operators are investigated on the Bloch space $\mathcal{B}$, the little Bloch space $\mathcal{B }_0 $ and the Besov Space $\mathcal{B}_p$. Let $\mathbb{U}$ be the unit disk on the complex plane $\mathbb{C}$ and $\psi$ be a function on the space of holomorphic functions $H(\mathbb{U})$, our goal is to find out when the multiplication operator $M_{ \psi}$ is power bounded, mean ergodic and uniformly mean ergodic on $\mathcal{B}$, $\mathcal{B }_0 $ and $\mathcal{B}_p$.