On The maximal operators of Vilenkin-Fej\'er means on Hardy spaces

The main aim of this paper is to prove that when $0<p<1\mathrm{/}2$ the maximal operator $\overset{\sim }{\sigma }{p}^{\ast }f:=\underset{n\in $\mathbb{N}$}{% \sup }\frac{\left\vert \sigma{n}f\right\vert }{\left( n+1\right) ^{1/p-2}}$ is bounded from the martingale Hardy space $H_p$ to the space $L_p,$ where ${\sigma }_n$ is $n$-th Fej'er mean with respect to bounded Vilenkin system.