Abstract
In this paper, we present the new characterizations, in terms of the sequence $$\{z^j\}_{j=1}^\infty $$, about the boundedness and essential norm estimation for the products of differentiation and composition operators from logarithmic Bloch spaces to $$\mu $$-Bloch spaces on the unit disk. Then our main results are applied to show the boundedness of a non-trivial product operator $$C_\varphi D^m$$ with $$\varphi (z)=z^2$$.
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