Maximal operator of the Fejér means of triangular partial sums of two-dimensional WalshFourier series

It is proved that the maximal operator σδ# of the triangular-Fejér-means of a two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 > p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σδ _2n of a function f ∈ L1 converge a.e. to f . The maximal operator σδ# is bounded from the Hardy space H _1/2 to the space weak-L _1/2 and is not bounded from the Hardy space H _1/2 to the space L _1/2.