Abstract. The main aim of this paper is to prove that the maximal operator $\widetilde{\sigma }^*f:=\sup_{n\in P}{| \sigma_{n}f| \over\log^2(n+1)}$ is bounded from the Hardy space $H_{1/2}$ to the space $L_{1/2}$.

AMS Subject Classification (1991): 42C10

Keyword(s): Walsh function, Hardy space, Fejér means

Received August 27, 2007. (Registered under 6036/2009.)