Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the upper half-plane (Q554978)

Summary: Let \(\psi\) be a holomorphic mapping on the upper half-plane \(\Pi^+ = \{ z \in \mathbb C : \mathfrak I z > 0\}\) and \(\varphi\) be a holomorphic self-map of \(\Pi^+\). We characterize bounded weighted composition operators acting from the weighted Bergman space to the weighted-type space on the upper half-plane. Under a mild condition on \(\psi\), we also characterize the compactness of these operators.