### 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.

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