Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

Yu-Xia Liang¹ ; Chang-Jin Wang² ; Ze-Hua Zhou³

¹ School of Mathematical Sciences Tianjin Normal University Tianjin 300387, P.R. China
² School of Science Jimei University Xiamen, Fujian 361021, P.R. China
³ Department of Mathematics Tianjin University Tianjin 300072, P.R. China and Center for Applied Mathematics Tianjin University Tianjin 300072, P.R. China

Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 101-114

Résumé

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.

Détail

DOI : 10.4064/ap114-2-1

Keywords: mathbb denote space holomorphic functions unit ball mathbb subset mathbb varphi holomorphic self map mathbb mathbb weighted composition operator varphi mathbb defined varphi varphi investigate boundedness compactness varphi induced varphi acting zygmund spaces bloch little bloch spaces unit ball