Strong convergence theorem for Walsh-Kaczmarz-Fej\'er means
Nata Gogolashvili, K\'aroly Nagy, George Tephnadze
TL;DR
This paper proves that Fejér means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators on Hardy martingale spaces for certain p-values, advancing understanding of convergence in harmonic analysis.
Contribution
It establishes the boundedness of Fejér means for Walsh-Kaczmarz-Fourier series on Hardy martingale spaces for 0<p≤1/2, a novel result in this area.
Findings
Fejér means are uniformly bounded operators on H_p spaces for 0<p≤1/2
Advances the theory of Walsh-Kaczmarz-Fourier series convergence
Provides new tools for harmonic analysis on martingale spaces
Abstract
As main result we prove that Fej\'er means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators from the Hardy martingale space to the Hardy martingale space for
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