An Estimate of the Essential Norm of a Composition Operator from F(p,q,s) to ℬα in the Unit Ball

Abstract

Let Bn be the unit ball of ℂn and ϕ=(ϕ1,…,ϕn) a holomorphic self-map of Bn. Let 0<p,s<∞, -n-1<q<∞, q+s>-1, α>0, and let Cϕ be the composition operator between the space F(p,q,s) and α-Bloch space ℬα induced by ϕ. This paper gives an estimate of the essential norm of Cϕ. As a consequence, a necessary and sufficient condition for the composition operator Cϕ to be compact from F(p,q,s) to ℬα is obtained.