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Martingale Hardy spaces and some new weighted maximal operators of partial sums of Walsh–Fourier series

  • Davit Baramidze EMAIL logo
Published/Copyright: June 28, 2025
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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 operators indeed are bounded from the martingale Hardy space H p ( G ) to the Lebesgue space L p ( G ) for 0 < p < 1 . Moreover, we also prove the sharpness of this result. As a consequence, we obtain some new and well-known results.

MSC 2020: 42C10

Funding statement: The research was supported by the grant of The University of Georgia: “Mathematical Analysis and PDE’s on Lie groups”.

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Received: 2024-03-13
Revised: 2025-02-07
Accepted: 2025-03-07
Published Online: 2025-06-28

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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