Difference of composition operators in the Polydiscs

Abstract

This paper gives some simple estimates of the essential norm for the difference of composition operators induced by $\varphi$ and $\psi$ acting on bounded function space in the unit polydiscs $U^n$, where $\varphi (z)$ and $\psi (z)$be holomorphic self-maps of $U^n$. As its applications, a characterization of compact difference is given for composition operators acting on the bounded function spaces.

9 pages