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arXiv · 2302.12302

Weighted maximal operators of Fej\'er means of Walsh-Fourier series in the martingale Hardy space $H_{1/2}$

Nika Areshidze·Davit Baramidze·Lars-Erik Persson·George Tephnadze
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Abstract

In this paper we derive the restricted weighted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left(\left\vert \sigma _{k}F\right\vert/A^2_k\right)$ 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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Nika Areshidze, Davit Baramidze, Lars-Erik Persson, George Tephnadze. 2023-02-18. Weighted maximal operators of Fej\'er means of Walsh-Fourier series in the martingale Hardy space $H_{1/2}$. https://arxiv.org/abs/2302.12302

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