Fejér means of Vilenkin-Fourier series

Abstract

TThe main aim of this paper is to prove that there exist a martingale $f\in H_{1/2}$ such that Fejér means of Vilenkin-Fourier series of the martingale $f$ is not uniformly bounded in the space $L_{1/2}.$

Vilenkin system, Fejér means, martingale Hardy space

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• Sharp $\left(H_p,L_p\right)$ type inequalities of maximal operators of $T$ means with respect to Vilenkin systems with monotone coefficients
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