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arXiv · 2308.00794

Some new weak $(H_p-L_p)$ type inequality for weighted maximal operators of Walsh-Fourier series

David Baramidze·Lars-Erik Persson·Harpal Singh·George Tephnadze
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Abstract

In this paper we introduce some new weighted maximal operators of the partial sums of the Walsh-Fourier series. We prove that for some "optimal" weights these new operators indeed are bounded from the martingale Hardy space $H_{p}$ to the Lebesgue space $\text{weak}-L_{p},$ for $0<p<1.$ Moreover, we also prove sharpness of this result.

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David Baramidze, Lars-Erik Persson, Harpal Singh, George Tephnadze. 2023-06-26. Some new weak $(H_p-L_p)$ type inequality for weighted maximal operators of Walsh-Fourier series. https://arxiv.org/abs/2308.00794

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