Geodesic
Application of Ces\`aro 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

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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 $-1\alpha0$ 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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     author = {D. E. Men'shov},
     title = {Application of {Ces\`aro} summability methods of negative order to trigonometric {Fourier} series of summable and square summable functions},
     journal = {Sbornik. Mathematics},
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     year = {1974},
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D. E. Men'shov. Application of Ces\`aro 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/