1School of Mathematical Sciences Tianjin Normal University Tianjin 300387, P.R. China 2School of Science Jimei University Xiamen, Fujian 361021, P.R. China 3Department 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
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.
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
Affiliations des auteurs :
Yu-Xia Liang
1
;
Chang-Jin Wang
2
;
Ze-Hua Zhou
3
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
Yu-Xia Liang; Chang-Jin Wang; Ze-Hua Zhou. Weighted composition operators
from Zygmund spaces to Bloch spaces on the unit ball. Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 101-114. doi: 10.4064/ap114-2-1
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