Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces to Hμ∞

Abstract

In this note we express the norm of composition followed by differentiation $D{C}_{\phi }$ from the logarithmic Bloch and the little logarithmic Bloch spaces to the weighted space $H_{\mu }^{\infty }$ on the unit disk and give an upper and a lower bound for the essential norm of this operator from the logarithmic Bloch space to $H_{\mu }^{\infty }$.