Some new (Hp – Lp) type inequalities for weighted maximal operators of partial sums of Walsh–Fourier series

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https://hdl.handle.net/10037/30548
DOI
https://doi.org/10.1007/s11117-023-00989-3
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Date
2023-05-16
Type
Journal article
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Author
Baramidze, Davit; Persson, Lars-Erik; Tephnadze, George
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 Hp(G) to the Lebesgue space Lp(G), for 0<p<1. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.
Publisher
Springer Nature
Citation
Baramidze, Persson, Tephnadze. Some new (Hp- Lp) type inequalities for weighted maximal operators of partial sums of Walsh–Fourier series. Positivity (Dordrecht). 2023;27(3)
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Except where otherwise noted, this item's license is described as Attribution 4.0 International (CC BY 4.0)