Norm and essential norm of composition followed by differentiation from αα-Bloch spaces to Hμ∞

This note calculates the norm of composition followed by differentiation operator from the Bloch and the little Bloch space to the weighted space Hμ∞ on the unit disk, and gives an upper and a lower bound for the essential norm of the operator from the αα-Bloch space Bα,α>0Bα,α>0 to Hμ∞.