International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69-72, Pages 3941-3950
doi:10.1155/S0161171204403548
Essential norm of weighted composition operator between α-Bloch space and β-Bloch space in polydiscs
Songxiao Li1
and Xiangling Zhu2
1Department of Mathematics, Jiaying University, Meizhou 514015, Guangdong, China
2Department of Mathematics, Shantou University, Shantou 515063, Guangdong, China
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).