On operator \(P_\varphi^g\) from the logarithmic Bloch-type space to the mixed-norm space on the unit ball (Q961620)

Let \(g\in H(\mathbb{B})\), \(g(0)=0\), and \(\varphi\) be a holomorphic self-map of \(\mathbb{B}\), define the operator \(P_\varphi^g\) in the following way: \[ P_\varphi^gf(z)=\int_0^1f(\varphi(tz))g(tz)\frac{dt}{t},\quad f\in H(\mathbb{B}), z\in\mathbb{B}. \] In this paper, the author characterizes the boundedness and compactness of this operator from logarithmic Bloch-type spaces to mixed-norm spaces on \(\mathbb{B}\).