Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 132970, 22 pages
doi:10.1155/2010/132970
Research Article

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

Hong-Gang Zeng and Ze-Hua Zhou

Department of Mathematics, Tianjin University, Tianjin 300072, China

Received 29 June 2009; Revised 9 January 2010; Accepted 17 February 2010

Academic Editor: Michel C. Chipot

Copyright © 2010 Hong-Gang Zeng and Ze-Hua Zhou. 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 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.