Geodesic
Application of Cesàro summability methods of negative order to trigonometric Fourier series of summable and square summable functions
Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 497-515 
D. E. Men'shov. Application of Cesàro summability methods of negative order to trigonometric Fourier series of summable and square summable functions. Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 497-515. http://geodesic.mathdoc.fr/item/SM_1974_22_4_a1/
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     title = {Application of {Ces\`aro} summability methods of negative order to trigonometric {Fourier} series of summable and square summable functions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A Fourier series of a summable function is defined in the paper for which any sequence of Cesàro means of order $\alpha$ satisfying the inequality $-1<\alpha<0$ diverges on a set of positive measure. A Fourier series of a square summable function is also defined that has the same property for $\alpha$ satisfying the inequality $-1<\alpha<-\frac12$. Bibliography: 4 titles.

[1] A. Kolmogorov, “Sur les fonctions harmoniquees”, Fundam. Math., 7 (1925), 23–28

[2] A. Zigmund, Trigonometricheskie ryady, t. I, izd-vo «Mir», Moskva, 1965 | MR

[3] D. Menshov, “Primenenie metodov summirovaniya Chezaro otritsatelnogo poryadka k ryadam Fure-Lebega”, DAN SSSR, 210:2 (1973), 271–273

[4] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961 | MR