TL;DR
This paper demonstrates that for certain martingales in the Hardy space H_{1/2}, the Fejér means of their Vilenkin-Fourier series can be unbounded in the L_{1/2} space, highlighting limitations in convergence behavior.
Contribution
It proves the existence of martingales in H_{1/2} with unbounded Fejér means in L_{1/2}, revealing new insights into Fourier series convergence.
Findings
Fejér means are not uniformly bounded in L_{1/2} for some martingales in H_{1/2}
Existence of martingales with unbounded Fourier means in the specified spaces
Highlights limitations of Fejér summation in certain Hardy spaces
Abstract
TThe main aim of this paper is to prove that there exist a martingale such that Fej\'er means of Vilenkin-Fourier series of the martingale is not uniformly bounded in the space
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