On the maximal operators of Vilenkin-Fejer means

The main aim of this paper is to prove that the maximal operator overset{sim}{sigma}^{ast}f:=underset{n in P} supfrac{|sigma _nf|}{log^2 (n+1)} is bounded from the Hardy space H_{1/2} to the space L_{1/2}, where sigma _nf are Fejér means of bounded Vilenkin-Fourier series.