Integral-type operators between weighted Bergman spaces on the unit disk (Q2912664)

Let \(H({\mathbb D})\) be the space of all holomorphic functions on the open unit disk \(\mathbb D\) in the complex plane. The authors investigate integral-type operators \(I^{(n)}_{g}\) (\(n\in {\mathbb N}_{0}\), \(g\in H({\mathbb D})\)) of the form NEWLINE\[NEWLINE (I^{(n)}_{g}f)(\zeta)=\int_{0}^{z}f^{(n)}(\zeta)g(\zeta)\,d\zeta, \quad f\in H({\mathbb D}). NEWLINE\]NEWLINE They obtain necessary and sufficient conditions for boundedness and compactness of these operators acting between weighted Bergman spaces.