International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 71, Pages 3941-3950
doi:10.1155/S0161171204403548
Essential norm of weighted composition operator between α-Bloch space and β-Bloch space in polydiscs
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.
Abstract
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 ℂn. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space ℬα(𝔻n) and β-Bloch space ℬβ(𝔻n).