Communications of the
Korean Mathematical Society CKMS

Let $\varphi(z)=(\varphi_1(z),\cdot\cdot\cdot,\varphi_n(z))$ be a holomorphic self-map of $\mathbb{D}^{n}$, where $\mathbb{D}^{n}$ is the unit polydisk of $\mathbb{C}^n$. The sufficient and necessary conditions for a composition operator to be bounded and compact from the Hardy space $H^2(\mathbb{D}^{n})$ into $\alpha$-Bloch space $\mathcal{B}^\alpha(\mathbb{D}^{n})$ on the polydisk are given.

Keywords: composition operator, Hardy space, $\alpha$-Bloch space

MSC numbers: Primary 47B35; Secondary 30H05