Geodesic
On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions
Sbornik. Mathematics, Tome 22 (1974) no. 2, pp. 201-216 
S. V. Bochkarev. On the absolute convergence of Fourier series in bounded complete orthonormal systems of functions. Sbornik. Mathematics, Tome 22 (1974) no. 2, pp. 201-216. http://geodesic.mathdoc.fr/item/SM_1974_22_2_a3/
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     title = {On the absolute convergence of {Fourier} series in bounded complete orthonormal systems of functions},
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     url = {http://geodesic.mathdoc.fr/item/SM_1974_22_2_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the absolute convergence of Fourier series of absolutely continuous functions in arbitrary bounded complete orthonormal systems of functions. The results obtained are new even for the classical systems, namely the trigonometric system and the Walsh system. Bibliography: 8 titles.

[1] A. Zygmund, “Remarque sur la convergence absolute des séries de Fourier”, J. Lond. Math. Soc., 3 (1928), 194–196 | DOI | Zbl

[2] R. Salem, “On a theorem of Zygmund”, Duke Math. J., 10 (1943), 23–31 | DOI | MR | Zbl

[3] P. L. Ulyanov, “Reshennye i nereshennye problemy teorii trigonometricheskikh i ortogonalnykh ryadov”, Uspekhi matem. nauk, XIX:1 (115) (1964), 3–69 | MR

[4] I. Wik, “Criteria for absolute convergence of Fourier series of functions of bounded variations”, Trans. Amer. Math. Soc., 163 (1972), 1–24 | DOI | MR | Zbl

[5] S. V. Bochkarev, “O probleme Zigmunda”, Izv. AN SSSR, seriya matem., 37 (1973), 630–638 | Zbl

[6] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958

[7] S. Yano, “Lemma of Maircinkiewicz and Fourier series”, Tohoku Math. J., 11:2 (1959), 195–214 | DOI | MR

[8] J.-P. Kahane, Séries de Fourier also absolument convergentes, Springer-Verlag, Berlin–Heidelberg–New York, 1970 | MR | Zbl