Compact differences of composition operators from Bloch space to bounded holomorphic function space in the Polydisc

Let $\varphi$ and $\psi$ be holomorphic self-maps of the unit polydisc $U^n$ in the $n$-dimensional complex space, and denote by $C_{\varphi }$ and $C_{\psi }$ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators $C_{\varphi }-C_{\psi }$ from Bloch space to bounded holomorphic function space in the unit polydisc. Moreover the compactness of the difference is also characterized.