Norm and essential norm of composition followed by differentiation from α-Bloch spaces to H<inf>μ</inf>^∞

Abstract

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 α-Bloch space Bα, α > 0 to Hμ∞.