Geodesic
Properties of Cesàro means of negative order and of certain other $T$-means for Fourier series of continuous functions
Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 415-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main result established in this article is the following. Let $\alpha$ be an arbitrary negative nonintegral number. Then every continuous function can be changed on a set of arbitrarily small measure so that if $g(x)$ denotes the new function, then the sequence of the $T$-means (corresponding to the method $(C,\alpha)$) of the function $g(x)$ contains a subsequence converging uniformly to the function $g(x)$. Bibliography: 3 titles. 
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     author = {D. E. Men'shov},
     title = {Properties of {Ces\`aro} means of negative order and of certain other $T$-means for {Fourier} series of continuous functions},
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     year = {1971},
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D. E. Men'shov. Properties of Cesàro means of negative order and of certain other $T$-means for Fourier series of continuous functions. Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 415-441. http://geodesic.mathdoc.fr/item/SM_1971_15_3_a3/

[1] D. Menshov, “Sur la convergence uniforme des series de Fourier”, Matem. sb., 11(53) (1942), 67–96 | MR | Zbl

[2] H. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961

[3] A. Zigmund, Trigonometricheskie ryady, ch. I, Mir, Moskva, 1965 | MR