Wulan et al. 2009 , Wulan et al. characterized the compactness of composition operators on the Bloch space in the unit disk by the nth power of the induced analytic function. This paper will generalize the result to the Bloch type space in the polydisk.

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Let ϕ and ψ be holomorphic self-maps of the unit polydisc U n in the n-dimensional complex space, and denote by C ϕ and C ψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators C ϕ − C ψ from Bloch space to bounded holomorphic function space in the unit polydisc. The compactness of the difference is also characterized.2000 Mathematics subject classification: primary 47B38; secondary 26A16, 32A16, 32A26, 32A30, 32A37, 32A38, 32H02, 47B33.