Integral-type operators between \(\alpha \)-Bloch spaces and Besov spaces on the unit ball
Let \(H(\mathbb{B})\) denote the space of all holomorphic functions on the unit ball \(\mathbb{B}\subset\mathbb{C}\). For \(g\in H(\mathbb{B})\), the integral-type operators \(T_g\) and \(L_g\) are defined by \[ T_g(f)(z)=\int_0^1f(tz)\mathcal{R}g(tz)\frac{dt}{t} \quad{\text{and}}\quad L_g(f)(z)=\int_0^1\mathcal{R}f(tz)g(tz)\frac{dt}{t}, \quad z\in\mathbb{B}, \] where \(\mathcal{R}h\) is the radial derivative of \(h\). In this paper, the author characterizes the boundedness and compactness of \(T_g\) and \(L_g\) between \(\alpha\)-Bloch spaces and Besov spaces on the unit ball.
scientific article; zbMATH DE number 5772432
scientific article