It is proved that the maximal operator of the triangular Cesàro means of a two-dimensional Fourier series is bounded from the periodic Hardy space to for all 2/(2+α)<p≦∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular Cesàro means of a function converge a.e. to f.
 Berens, H., Li, Z., Xu, Y.2001On l−1 Riesz summability of the inverse Fourier integralIndag. Mathem.1241–53.