Geodesic
On convergence in the mean of Fourier series
Sbornik. Mathematics, Tome 38 (1981) no. 2, pp. 231-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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Various necessary and sufficient conditions are established for the convergence of the Fourier series of a function $f(x)\in L_{2\pi}$ in the norm of the space $L_{2\pi}$ (convergence in mean with exponent $1$). Bibliography: 16 titles. 
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G. A. Fomin. On convergence in the mean of Fourier series. Sbornik. Mathematics, Tome 38 (1981) no. 2, pp. 231-244. http://geodesic.mathdoc.fr/item/SM_1981_38_2_a4/

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[11] S. A. Telyakovskii, G. A. Fomin, “O skhodimosti v metrike $L$ ryadov Fure s kvazimonotonnymi koeffitsientami”, Trudy Matem. in-ta im. V. A. Steklova, CXXXIV (1975), 310–313

[12] G. A. Fomin, “O nekotorykh usloviyakh skhodimosti ryadov Fure v metrike $L$”, Matem. zametki, 21:4 (1977), 587–592 | MR | Zbl

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[16] J. Ch. Vallee-Poussin, Leçons sur l'approximation des fonctions d'une variable reelle, Paris, 1919 | Zbl