Geodesic
Unbounded divergence of Fourier series of continuous functions
Matematičeskie zametki, Tome 7 (1970) no. 1, pp. 7-18 
V. V. Buzdalin. Unbounded divergence of Fourier series of continuous functions. Matematičeskie zametki, Tome 7 (1970) no. 1, pp. 7-18. http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a1/
@article{MZM_1970_7_1_a1,
     author = {V. V. Buzdalin},
     title = {Unbounded divergence of {Fourier} series of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {7--18},
     year = {1970},
     volume = {7},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For any given set $E\subset[0,\,2\pi)$, of measure zero, a function $f(t)\in C(0,\,2\pi)$, is constructed whose Fourier series is unboundedly divergent on $E$. If $E$ is closed, there is a function $\varphi(t)\in C(0,2\pi)$, whose Fourier series diverges unboundedly on $E$ and converges on $[0,2\pi)\setminus E$.