On the convergence of double Fourier series of functions in LP[0, 1]2, where p=(p1, p2)

Abstract

Pointwise convergence of double trigonometric Fourier series of functions in the Lebesgue space Lp[0, 2π]2 was studied by M.I.Dyachenko. In this paper, we also consider the problems of the convergence of double Fourier series in Pringsheim's sense with respect to the trigonometric as well as the Walsh systems of functions in the Lebesgue space LP[0, 1]2, p=(p1, p2), endowed with a mixed norm, in the particular case when the coefficients of the series in question are monotone with respect to each of the indices.