Let $H({\Bbb D})$ denote the space of all analytic functions on the unit disk ${\Bbb D}$ in the complex plane $ {\Bbb C}$, $\psi_1, \psi_2\in H({\Bbb D}),$ $n$ be a nonnegative integer, $\varphi$ an analytic self-map of $ {\Bbb D}$ and $\mu$ a weight. We study the boundedness and compactness of a product-type operator which is defined by
from the mixed norm space to Zygmund-type spaces.