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

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