On trigonometric Fourier series
Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 521-546 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper studies the problem of the convergence and $(C,\alpha)$ summability of simple and multiple trigonometric Fourier series. Bibliography: 21 titles.
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L. V. Zhizhiashvili. On trigonometric Fourier series. Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 521-546. http://geodesic.mathdoc.fr/item/SM_1976_29_4_a5/

[1] L. V. Zhizhiashvili, “O nekotorykh voprosakh iz teorii prostykh i kratnykh trigonometricheskikh i ortogonalnykh ryadov”, Uspekhi matem. nauk, XXVIII:2 (170) (1973), 65–119

[2] N. K. Bari, Trigonometricheskie ryady, Gostekhizdat, Moskva, 1961 | MR

[3] P. Fatou, “Séries trigonométriques et séries de Taylor”, Acta Math., 30 (1906), 335–400 | DOI | MR | Zbl

[4] G. H. Hardy, J. E. Littlewood, “Abel's theorem and its convergence”, Proc. London Math. Soc., 18 (1919), 205–235 | DOI | Zbl

[5] G. H. Hardy, J. E. Littlewood, “Some new convergence criteria for Fourier series”, J. London Math. Soc., 7 (1932), 252–256 | DOI | Zbl

[6] G. H. Hardy, J. E. Littlewood, “Some new convergence criteria for Fourier series”, Ann. Scole Norm. Super de Pisa, 3 (1934), 43–62 | MR | Zbl

[7] R. Paley, “On Fourier series with positive coefficients”, J. London, Math. Soc., 7 (1932), 205–208 | DOI | Zbl

[8] O. Szasz, “Zur Konvergenztheorie der Fourierschen Reihen”, Acta Math., 61 (1933), 185–201 | DOI | MR | Zbl

[9] A. Zygmund, “Sur la sommabilité des séries de Fourier des fonctions vérifiant la condition de Lipschitz”, Bull. de l'Acad. Polon., 1925, 1–9 | Zbl

[10] G. H. Hardy, J. E. Littlewood, “A convergence criterion for Fourier series”, Math. Z., 28 (1928), 612–634 | DOI | MR | Zbl

[11] K. Yano, “On Hardy and Littlewood's theorem”, Proc. Japan Acad., 33 (1957), 73–74 | DOI | MR | Zbl

[12] L. V. Zhizhiashvili, Sopryazhennye funktsii i trigonometricheskie ryady, Tbilisi, 1969 | MR

[13] M. M. Lekishvili, “Teoremy vlozheniya i priblizhenie funktsii srednimi”, Soobsch. AN GruzSSR, 71:1 (1973), 49–52 | Zbl

[14] T. I. Akhobadze, O skhodimosti i summiruemosti prostykh i kratnykh ryadov Fure, Kand. dissertatsiya, Tbilisi, 1973

[15] L. V. Zhizhiashvili, “O summiruemosti kratnykh trigonometricheskikh ryadov Fure”, Soobsch. AN GruzSSR, 75:1 (1974), 49–51

[16] L. V. Zhizhiashvili, “O prostykh i kratnykh ryadakh Fure”, DAN SSSR, 225:2 (1975), 256–258 | MR | Zbl

[17] A. Zigmund, Trigonometricheskie ryady, t. 1, Fizmatgiz, Moskva, 1965

[18] G. Páe Névai, “Fourier-sorok és interpoláció”, Matem. Lapok, 3–4 (1972), 261–290

[19] M. A. Subkhankulov, L. I. Krainova, “Granichnye znacheniya integrala Puassona i skhodimost ryadov Fure”, DAN UzSSR, seriya fiz.-matem. n., 1967, no. 1, 23–31 | Zbl

[20] W. H. Young, “Konvergenzbedingungen für die verwandte Reihe einer Fourierschen Reihe”, Münchener Sitzungsber., 41 (1911), 361–371 | Zbl

[21] L. Cesari, “Sulle cerie di Fourier della fonzioni Lipshitziane di piu variabili”, Ann. Scole Norm. Super de Pisa, 7 (1938), 279–295 | MR | Zbl