Title: Hausdorff operators on holomorphic Hardy spaces and applications,
Abstract: The aim of this paper is to characterize the nonnegative functions $\varphi$
defined on $(0,\infty)$ for which the Hausdorff operator
$$\mathscr H_\varphi f(z)= \int_0^\infty
f\left(\frac{z}{t}\right)\frac{\varphi(t)}{t}dt$$ is bounded on the Hardy
spaces of the upper half-plane $\mathcal H_a^p(\mathbb C_+)$, $p\in[1,\infty]$.
The corresponding operator norms and their applications are also given.