Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series

Abstract

It is proved that the maximal operator of the triangular-Fejér-means of a two-dimensional Walsh–Fourier series is bounded from the dyadic Hardy space to for all and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means of a function converge a.e. to . The maximal operator is bounded from the Hardy space to the space weak- and is not bounded from the Hardy space to the space .