Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball
Volume 114 / 2015
Annales Polonici Mathematici 114 (2015), 101-114
MSC: Primary 47B38; Secondary 32A37, 32A38, 32H02, 47B33.
DOI: 10.4064/ap114-2-1
Abstract
Let $H(\mathbb {B})$ denote the space of all holomorphic functions on the unit ball $\mathbb {B}\subset \mathbb {C}^n.$ Let $\varphi $ be a holomorphic self-map of $\mathbb {B}$ and $u\in H(\mathbb {B})$. The weighted composition operator $uC_\varphi $ on $H(\mathbb {B})$ is defined by $$ uC_\varphi f(z)=u(z) f(\varphi (z)). $$ We investigate the boundedness and compactness of $uC_\varphi $ induced by $u$ and $\varphi $ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
