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Weighted maximal operators of Fejér means of Walsh-Fourier series in the martingale Hardy space $H_{1/2}$ (2302.12302v1)

Published 18 Feb 2023 in math.CA

Abstract: In this paper we derive the restricted weighted maximal operator, defined by ${\sup }{k\in \mathbb{N}}\left(\left\vert \sigma _{k}F\right\vert/A2_k\right)$ of Fej\'er means of Walsh-Fourier series and prove that the it is bounded from the martingale Hardy space $H{1/2}(G)$ to the Lebesgue space $L_{1/2}(G).$ The sharpness of this result is also proved. As a consequence we obtain some new and and well-know results.

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