Essential Norms of Weighted Differentiation Composition Operators between Zygmund Type Spaces and Bloch Type Spaces

Abstract

We study boundedness of weighted differentiation composition operators $D_{\varphi,u}^k$ between Zygmund type spaces $\mathcal{Z}^\alpha$ and Bloch type spaces $\mathcal{B}^\beta$. We also give essential norm estimates of such operators in different cases of $k\in \mathbb{N}$ and $0<\alpha, \beta <\infty$. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.