Difference of composition operators in the Polydiscs

This paper gives some simple estimates of the essential norm for the difference of composition operators induced by $\phi$ and $\psi$ acting on bounded function space in the unit polydiscs $U^n$, where $\phi(z)$ 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.