Geodesic
On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 497-505 
N. Yu. Antonov. On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 497-505. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a1/
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     title = {On {Divergence} {Almost} {Everywhere} of {Fourier} {Series} of {Continuous} {Functions} of {Two} {Variables}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider one type of convergence of double trigonometric Fourier series intermediate between convergence over squares and $\lambda$-convergence for $\lambda>1$. We construct an example of continuous functions of two variables, Fourier series of which diverges in this sense, almost everywhere.

[1] Tevzadze N. R., “On the convergence of double Fourier series of quadratic summable functions”, Soobshcheniia Akad. Nauk Gruzin. SSR, 58:2 (1970), 277–279 (in Russian) | MR | Zbl

[2] Fefferman C., “On the convergence of multiple Fourier series”, Bull. Amer. Math. Soc., 77:5 (1971), 744–745 | DOI | MR | Zbl

[3] Fefferman C., “On the divergence of multiple Fourier series”, Bull. Amer. Math. Soc., 77:2 (1971), 191–195 | DOI | MR | Zbl

[4] Bakhbukh M., Nikishin E. M., “The convergence of the double Fourier series of continuous functions”, Siberian Math. J., 14:6 (1973), 832–839 | DOI | MR | Zbl

[5] Bakhvalov A. N., “Divergence everywhere of the Fourier series of continuous functions of several variables”, Sb. Math., 188:8 (1997), 1153–1170 | DOI | DOI | MR | Zbl

[6] Bakhvalov A. N., “$\lambda$-divergence of the Fourier series of continuous functions of several variables”, Math. Notes, 72:3–4 (2002), 454–465 | DOI | DOI | MR | Zbl

[7] Stepanec A. I., “Estimates of deviations of partial Fourier sums on classes of continuous periodic functions of several variables”, Math. USSR Izv., 17:2 (1981), 369–403 | DOI | MR | Zbl

[8] Zygmund A., Trigonometric series, v. 2, Cambridge Univ. Press, 1959 | MR | MR | Zbl