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

Abstract

The main aim of this paper is to prove that the maximal operator $\overset{% \sim }{\sigma }^{*}f:=\underset{n\in P}{\sup }\frac{\left| \sigma_{n}f\right| }{\log ^{2}\left( n+1\right) }$ is bounded from the Hardy space $H_{1/2}$ to the space $L_{1/2}$, where $\sigma_{n}f$ is Fej\'er means of bounded Vilenkin-Fourier series.