The product-type operators from logarithmic Bloch spaces to Zygmund-type spaces

Abstract

The boundedness and compactness of a product-type
operator, recently introduced by S. Stevi\' c, A. Sharma and R. Krishan,
$$T^n_{\psi_{1},\psi_{2},\varphi}f(z)=\psi_1(z)f^{(n)}(\varphi(z))+\psi_2(z)f^{(n+1)}(\varphi(z)),~f\in H(\mathbb{D}),$$
from the logarithmic Bloch spaces to Zygmund-type spaces are characterized, where $\psi_1, \psi_2\in H(\mathbb{D}),$
$\varphi$ is an analytic self-map of $ \mathbb{D}$ and $n$ a positive integer.