Geodesic
On~some properties of orthogonal systems
Izvestiya. Mathematics , Tome 43 (1994) no. 2, pp. 261-289.

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Questions of uniform convergence and convergence in the $L^p$-metric are considered for series in complete orthonormal systems of functions in the classes $C_{[0,1]}$ and $L^p$, $p2$. 
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M. G. Grigoryan. On~some properties of orthogonal systems. Izvestiya. Mathematics , Tome 43 (1994) no. 2, pp. 261-289. http://geodesic.mathdoc.fr/item/IM2_1994_43_2_a3/

[1] Luzin N. N., “K osnovnoi teoreme integralnogo ischisleniya”, Matem. sb., 28:2 (1912), 266–294

[2] Menshov D. E., “O ravnomernoi skhodimosti ryadov Fure”, Matem. sb., 11(53) (1942), 67–96 | Zbl

[3] Menshov D. E., “O ryadakh Fure ot summiruemykh funktsii”, Tr. Mosk. matem. ob-va, 1, 1952, 5–38 | Zbl

[4] Talalyan A. A., “Polnye sistemy bezuslovnoi skhodimosti v slabom smysle”, Izv. AN SSSR. Ser. matem., 28:3 (1964), 713–720

[5] Oskolkov K. M., “Ravnomernyi modul nepreryvnosti summiruemykh funktsii na mnozhestvakh polozhitelnoi mery”, DAN SSSR, 229:2 (1976), 304–306 | MR | Zbl

[6] Arutyunyan F. G., “O ryadakh po sisteme Khaara”, DAN ArmSSR, 42:3 (1966), 134–140 | MR | Zbl

[7] Kashin B. S., Kosheleva G. G., “Ob odnom podkhode k teoremam ob ispravlenii”, Vest. MGU. Ser. mat.-mekh., 1988, no. 1, 6–8 | MR

[8] Tsereteli O. D., “O suschnosti pochti vsyudu ryadov Fure”, Soobsch. AN GruzSSR, 57:1 (1970), 21–24 | Zbl

[9] Price J. J., “Walsh series and adjustment of fonctions on small sets”, Illinois J. Math., 13:1 (1969), 131–136 | MR | Zbl

[10] Kheladze Sh. V., “Skhodimost ryadov Fure pochti vsyudu i v smysle metriki $L$”, Matem. sb., 107(149):2 (1978), 245–258 | MR | Zbl

[11] Gulisashvili A. B., “Perestroiki, rasstanovka znakov i skhodimost posledovatelnostei operatorov”, Zap. nauchn. seminarov LOMI, 107, 1982, 45–49 | MR

[12] Grigoryan M. G., “O skhodimosti v metrike $L^p$, $0

1$, sfericheskikh chastichnykh summ dvoinykh ryadov Fure”, Matem. zametki, 33:4 (1983), 517–528 | MR | Zbl

[13] Grigoryan M. G., “O skhodimosti pochti vsyudu dvoinykh ryadov Fure summiruemykh funktsii”, Anal. Math., 11:3 (1985), 201–216 | DOI | MR | Zbl

[14] Grigoryan M. G., “O skhodimosti ryadov Laplasa i Fure”, DAN SSSR, 315:2 (1990), 265–266 | Zbl

[15] Menshov D. E., “O ryadakh Fure nepreryvnykh funktsii”, Uch. zapiski. Matematika, 148, 1951, 108–132 | MR

[16] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[17] Grigoryan M. G., “On the convergence of Fourier series in the metrice of”, Anal. Math., 17 (1991) | MR | Zbl

[18] Grigoryan M. G., “O skhodimosti v metrike i pochti vsyudu ryadov Fure i o koeffitsientakh Fure summiruemykh funktsii”, Izv. AN ArmSSR. Ser. matem., XXVI:1 (1991), 28–35

[19] Grigoryan M. G., “O skhodimosti ryadov Fure–Uolsha v metrike $L^1$ i pochti vsyudu”, Izv. VUZov, 1990, no. 11, 9–18 | MR | Zbl

[20] Ulyanov P. L., “O ryadakh po perestavlennoi trigonometricheskoi sisteme”, Izv. AN SSSR. Ser. matem., 22:4 (1958), 515–542 | MR

[21] Grigoryan M. G., “O skhodimosti v metrike $L$ i pochti vsyudu ryadov Fure po polnym ortonormirovannym sistemam”, Matem. sb., 181:8 (1990), 1011–1030

[22] Kashin B. S., “Ob odnoi polnoi ortonormirovannoi sisteme”, Matem. sb., 99(141) (1976), 356–365 | Zbl

[23] Kazaryan K. S., “O nekotorykh voprosakh teorii ortogonalnykh ryadov”, Matem. sb., 1982, no. 2, 278–294 | MR | Zbl

[24] Olevskii A. M., “Ryady Fure nepreryvnykh funktsii po ogranichennym ortonormirovannym sistemam”, Izv. AN SSSR. Ser. matem., 30:2 (1966), 387–432 | MR | Zbl

[25] Carleson L., “On corvergence and growth of partial sums of Fourier series”, Acta Math., 116 (1966), 135–157 | DOI | MR | Zbl

[26] Riss M., “Sur les fonctions conjugees”, Math. Zeit, 27 (1927), 218–244

[27] Kolmogorov A. H., “Sur les fonctions harmoniques conjuguees et les series de Fourier”, FM, 7 (1925), 23–28

[28] Zhizhiashvili L. B., “O nekotorykh voprosakh iz teorii prostykh i kratnykh trigonometricheskikh i ortogonalnykh ryadov”, UMN, 28:2 (1973), 65–119 | MR

[29] Fefferman C., “On the divergence of multiple Fourier series”, Bull Amer. Math. Soc., 77:2 (1971), 191–195 | DOI | MR | Zbl

[30] Fefferman C., “The multiple problem for the ball”, Ann. Math., 94:2 (1971), 330–336 | DOI | MR | Zbl

[31] Getsadze R. D., “O raskhodimosti po mere obschikh kratnykh ortogonalnykh ryadov Fure”, DAN SSSR, 306:1 (1989) | Zbl

[32] Garsia A. M., Topis in almost everywhere convergence, Markham, Chicago, 1970 | MR | Zbl