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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[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