Geodesic
On convergence in the mean of Fourier series
Sbornik. Mathematics, Tome 38 (1981) no. 2, pp. 231-244

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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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     author = {G. A. Fomin},
     title = {On convergence in the mean of {Fourier} series},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1981},
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     url = {http://geodesic.mathdoc.fr/item/SM_1981_38_2_a4/}
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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/