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Hausdorff operators on Hardy spaces

E. Liflyand

Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel

Abstract: 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.

Keywords and phrases: Hausdorff operator, power series, Fourier transform, Hardy space.

MSC: 47B38, 42B10, 46E30

Received: 11.05.2013

Language: English