Geodesic
Refinement of the Dirichlet–Jordan and Young's
Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 777-791 
A. S. Belov; S. A. Telyakovskii. Refinement of the Dirichlet–Jordan and Young's. Sbornik. Mathematics, Tome 198 (2007) no. 6, pp. 777-791. http://geodesic.mathdoc.fr/item/SM_2007_198_6_a1/
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     title = {Refinement of the {Dirichlet{\textendash}Jordan} and {Young's}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions on an increasing sequence of positive integers $\{n_j\}$ ensuring that the Fourier series of a function of bounded variation has uniformly bounded sums of the absolute values of the blocks of terms with harmonics from $n_j$ to $n_{j+1}-1$ are established. Bibliography: 9 titles.

[1] S. A. Telyakovskii, “O chastnykh summakh ryadov Fure funktsii ogranichennoi variatsii”, Teoriya priblizhenii. Garmonicheskii analiz, Tr. MIAN, 219, Nauka, M., 1997, 378–386 | MR | Zbl

[2] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 ; N. K. Bary, A treatise on trigonometric series, vols. I, II, Pergamon Press, Oxford–London–New York–Paris–Frankfurt, 1964 | MR | MR | Zbl

[3] S. A. Telyakovskii, “O ravnomernoi skhodimosti ryadov Fure funktsii ogranichennoi variatsii”, Funktsionalnye prostranstva, garmonicheskii analiz, differentsialnye uravneniya, Tr. MIAN, 232, Nauka, M., 2001, 318–326 | MR | Zbl

[4] S. A. Telyakovskii, “O skorosti skhodimosti ryadov Fure funktsii ogranichennoi variatsii”, Matem. zametki, 72:6 (2002), 949–953 | MR | Zbl

[5] R. Bojanić, “An estimate of the rate of convergence for Fourier series of functions of bounded variation”, Publ. Inst. Math. (Beograd) (N.S.), 26(40) (1979), 57–60 | MR | Zbl

[6] S. A. Telyakovskii, “Usilenie teoremy Dirikhle –Zhordana o skhodimosti ryadov Fure funktsii ogranichennoi variatsii”, Mezhdunarodnaya konferentsiya “Funktsionalnye prostranstva, teoriya priblizhenii, nelineinyi analiz”, posvyaschennaya stoletiyu akademika S. M. Nikolskogo. Tezisy dokladov (Moskva, 2005), MIAN, M., 2005, 221

[7] A. Yu. Popov, S. A. Telyakovskii, “K otsenkam chastnykh summ ryadov Fure funktsii ogranichennoi variatsii”, Izv. vuzov. Matem., 2000, no. 1, 51–55 | MR | Zbl

[8] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967 ; K. Yosida, Functional analysis, Academic Press, New York; Springer-Verlag, Berlin, 1965 | MR | Zbl | MR | Zbl

[9] A. Zigmund, Trigonometricheskie ryady, t. I, Mir, M., 1965 ; A. Zygmund, Trigonometric series, vol. I, Cambridge Univ. Press, Cambridge, 1959 | MR | Zbl | MR | Zbl