Essential Norms of Composition Followed by Differentiation Operators from Bloch-type Spaces into Bers-type Spaces

Hamid Vaezi, Mohamad Naghlisar

Abstract

In this paper we consider the composition followed by differentation operator $DC_{\varphi}$ from Bloch-type space $B^{\alpha}$ into Bers-type space $H_{\beta}^{\infty}$. We give necessary and sufficient conditions for the boundedness and compactness of the above operator. We also give essential norm of such an operator in term of $\varphi$.