Hausdorff operators on Hardy spaces

Hausdorff operators (Hausdorff summability methods) appeared long ago aiming to solve certain classical problems in analysis. Modern theory of Hausdorff operators started with the work of Siskakis in complex analysis setting and with the work of Liflyand–Móricz in the Fourier transform setting. In this paper a survey of the main results on Hausdorff operators in various settings is given. Many open problems in the subject are formulated.