COMPOSITION OPERATORS FROM HARDY SPACES INTO α-BLOCH SPACES ON THE POLYDISK
COMPOSITION OPERATORS FROM HARDY SPACES INTO α-BLOCH SPACES ON THE POLYDISK
Let <TEX>${\varphi}(z)\;=\;({\varphi}_1(Z),{\cdots},{\varphi}_n(Z))$</TEX> be a holomorphic selfmap of <TEX>$\mathbb{D}^n$</TEX>, where <TEX>$\mathbb{D}^n$</TEX> is the unit polydisk of <TEX>$\mathbb{C}^n$</TEX>. The sufficient and necessary conditions for a composition operator to be bounded and compact from the Hardy space <TEX>$H^2(\mathbb{D}^n)$</TEX> into <TEX>$\alpha$</TEX>-Bloch space <TEX>$\beta^{\alpha}(\mathbb{D}^n)$</TEX> on the polydisk are given.