Abstract
In this paper, we give a new characterization for the boundedness of the product of differentiation and composition operators \({C_\varphi D^m}\) acting on Bloch-type spaces and obtain an estimate for its essential norm in terms of the sequence \({\{z^n\}^{\infty}_{n=1}}\), from which the sufficient and necessary condition of compactness of the operator \({C_\varphi D^m}\) follows immediately.
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