Objective To characterize the boundedness and essential norms of the product of differentiation and composition operators CφDm on logarithmic Bloch type spaces.Methods A bounded sequence { zn } n=1 was used to characterize the boundedness of the product of differential composite operators CφDm on logarithmic Bloch type spaces and the operator theory in functional analysis,such as the properties of compact operators.Results The es-sential norm of the product of differentiation and composition operators CφDm on the logarithmic Bloch type was obtained.Here m is a nonnegative positive integer,and the product of the differentiation and composition operator CφDm is defined by CφDmf=f(m)°φ.Conclusion If the product of differential composite operators CφDm on logarith-mic Bloch type spaces is bounded,the essential norm of C Dm may be characterized by the characteristics of the bounded sequence { zn}.
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