Integral-type operators acting between weighted-type spaces on the unit ball
Let \(\mathbb{B}\) denote the unit ball in \(\mathbb{C}^n\) and \(H(\mathbb{B})\) the space of all holomorphic functions on \(\mathbb{B}\). In this paper, the authors study the boundedness and compactness of the integral-type operators \[ I_\varphi^gf(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{dt}{t},\quad z\in \mathbb B, \] where \(g\in H(\mathbb{B})\), \(g(0)=0\), \(\varphi\) is a holomorphic self-map of \(\mathbb{B}\) and \(\Re f\) is the radial derivative of the function \(f\), between weighted-type spaces on the unit ball.
scientific article; zbMATH DE number 5649895
scientific article