We give a new characterization for the boundedness of composition operator followed by differentiation operator acting on Bloch-type spaces and calculate its essential norm in terms of the $n$-th power of the induced analytic self-map on the unit disk. From which some sufficient and necessary conditions of compactness of the operator follow immediately.
"New estimate of essential norm of composition followed by differentiation between Bloch-type spaces." Banach J. Math. Anal. 8 (1) 118 - 137, 2014. https://doi.org/10.15352/bjma/1381782092