Convergence of double Fourier series with coefficients of generalized bounded variation

Abstract

We extend the class of double null sequences of complex numbers that are of bounded variation and prove the almost everywhere pointwise convergence as well as the convergence in the L r(T 2) -metric for 0 < r < 1 of double Fourier series with such coefficients. We study mainly convergence in Pringsheim's sense, either unrestricted or restricted, but regular convergence is also considered.