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Let $\phi$ and $\psi$ be holomorphic self-maps of the unit polydisc $U^n$ inthe $n$-dimensional complex space, and denote by $C_{\phi}$ and $C_{\psi}$ theinduced composition operators. This paper gives some simple estimates of theessential 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.

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