International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 71, Pages 3941-3950

Essential norm of weighted composition operator between α-Bloch space and β-Bloch space in polydiscs

Li Songxiao1 and Zhu Xiangling2

1Department of Mathematics, Jiaying University, Meizhou 514015, Guangdong, China
2Department of Mathematics, Shantou University, Shantou 515063, Guangdong, China

Received 29 March 2004

Copyright © 2004 Li Songxiao and Zhu Xiangling. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let φ(z)=(φ1(z),,φn(z)) be a holomorphic self-map of 𝔻n and ψ(z) a holomorphic function on 𝔻n, where 𝔻n is the unit polydiscs of n. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space α(𝔻n) and β-Bloch space β(𝔻n).