-convergence almost everywhere of double Fourier series

Abstract

In this paper we consider -convergence of double Fourier series (-convergence of a double number series implies that it converges in the sense of Pringsheim, over spheres, and so on.) Unextendable classes of Weyl multipliers for -convergence almost everywhere are described. In addition, close to exact sufficient conditions for -convergence almost everywhere in the spaces and are found.