Geodesic
On the convergence of double Fourier series of discontinuous functions
Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 501-510 
R. A. Avetisyan. On the convergence of double Fourier series of discontinuous functions. Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 501-510. http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a1/
@article{MZM_1975_17_4_a1,
     author = {R. A. Avetisyan},
     title = {On the convergence of double {Fourier} series of discontinuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {501--510},
     year = {1975},
     volume = {17},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we obtain a formula for the computation of the rectangular partial sums of a double Fourier series of a function of two variables at the point (0, 0), having a discontinuity along any ray at this point. We also give an estimate of the remainder in the abovementioned formula.