Geodesic
Remarks on estimating the Lebesgue functions of an orthonormal system
Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 57-62 
B. S. Kashin. Remarks on estimating the Lebesgue functions of an orthonormal system. Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 57-62. http://geodesic.mathdoc.fr/item/SM_1979_35_1_a4/
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In this paper we clarify the relationship between lower bounds for Lebesgue functions and multiplicative inequalities of Gagliardo–Nirenberg type. We give simple proofs of some theorems on Lebesgue functions. Bibliography: 10 titles.

[1] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958 | MR

[2] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, izd-vo “Nauka”, Moskva, 1975 | MR | Zbl

[3] A. M. Olevski, Fourier series with Respect to General orthogonal systems, Springer-Verlag, Berlin, 1975 | MR | Zbl

[4] A. M. Olevskii, “Ryady Fure nepreryvnykh funktsii po polnym ortonormalnym sistemam”, Izv. AN SSSR, seriya matem., 30 (1966), 387–432 | MR | Zbl

[5] A. M. Olevskii, “Ryady Fure i funktsii Lebega”, Uspekhi matem. nauk, XXII:3(135) (1967), 237–239 | MR

[6] S. V. Bochkarev, “Ob absolyutnoi skhodimosti ryadov Fure po ogranichennym polnym ortonormirovannym sistemam funktsii”, Matem. sb., 93(135) (1974), 203–217 | MR | Zbl

[7] S. V. Bochkarev, “Ob absolyutnoi skhodimosti ryadov Fure po ogranichennym sistemam”, Matem. zametki, 15:3 (1974), 363–370 | MR | Zbl

[8] B. S. Kashin, “O koeffitsientakh razlozheniya odnogo klassa funktsii po polnym sistemam”, Sib. matem. zh., 18:1 (1977), 122–131 | MR | Zbl

[9] S. V. Bochkarev, “Logarifmicheskii rost srednikh arifmeticheskikh ot funktsii Lebega ogranichennykh ortonormirovannykh sistem”, DAN SSSR, 223:1 (1975), 16–19 | MR | Zbl

[10] S. V. Bochkarev, “Raskhodyaschiisya na mnozhestve polozhitelnoi mery ryad Fure dlya proizvolnoi ogranichennoi ortonormirovannoi sistemy”, Matem. sb., 98(140) (1975), 436–449 | MR | Zbl