2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71432It is proved that the complex double Fourier series of an integrable function $f(x,y)$ with coefficients $\{c_{jk}\}$ satisfying certain conditions, will converge in $L^{1}$-norm. The conditions used here are the combinations of Tauberian condition of Hardy--Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.9 pages, no figures, no tablesFunctional Analysis42A20, 42A32text