Integral representation of vertical operators on the Bergman space over the upper half-plane

Let $\Pi $ denote the upper half-plane. In this article, we prove that every vertical operator on the Bergman space $\mathcal{A}^2(\Pi )$ over the upper half-plane can be uniquely represented as an integral operator of the form \begin{equation*} \left(S_\varphi f\right)(z) = \int _{\Pi } f(w) \varp...

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