Geodesic
Limits of indeterminacy in measure of $T$-means of trigonometric series
Sbornik. Mathematics, Tome 10 (1970) no. 4, pp. 441-474 
D. E. Men'shov. Limits of indeterminacy in measure of $T$-means of trigonometric series. Sbornik. Mathematics, Tome 10 (1970) no. 4, pp. 441-474. http://geodesic.mathdoc.fr/item/SM_1970_10_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following theorem is proved. Let $F(x)$ and $G(x)$ be arbitrary measurable functions such that $G(x)\leqslant F(x)$ almost everywhere on $[-\pi,\pi]$, and let $T$ be an arbitrary row-finite summation method defined by a real matrix. Then there exists a trigonometric series whose coefficients tend to zero and such that the limits of indeterminacy of its $T$-means are exactly $F(x)$ and $G(x)$. Bibliography: 8 titles.

[1] D. Menshov, “O skhodimosti po mere trigonometricheskikh ryadov”, Trudy matem. in-ta im. V. A. Steklova AN SSSR, 32, 1950, 3–98 | MR | Zbl

[2] D. Menshov, “Predely neopredelennosti po mere trigonometricheskikh i ortogonalnykh ryadov”, Trudy matem. in-ta im. V. A. Steklova AN SSSR, 99, 1967, 3–62

[3] G. Khardi, Raskhodyaschiesya ryady, IL, Moskva, 1951

[4] D. Menshov, “Predely neopredelennosti po mere $T$-srednikh dlya trigonometricheskikh ryadov”, DAN SSSR, 176:3 (1967), 518–521

[5] D. Menshov, “O predelakh neopredelennosti chastnykh summ universalnykh trigonometricheskikh ryadov”, Uchenye zapiski MGU, matem., 165, 1954, 3–33 | MR

[6] D. Menshov, “O predelnykh funktsiyakh trigonometricheskogo ryada”, Trudy Mosk. matem. ob-va, 7, 1958, 291–334 | Zbl

[7] D. Menshov, “Ob universalnykh posledovatelnostyakh funktsii”, Matem. sb., 65(107) (1964), 272–312

[8] N. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961 | MR