Geodesic
Necessary and sufficient conditions for the imbedding of some classes of functions
Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 388-400.

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Necessary and sufficient conditions are found for membership of a function $f(x)\in L^p(0,1)$ in the class $L^q\Phi (L)$, $1\le p\le q\infty$. A connection is established between the modulus of continuity $\omega(\delta,f^*)$ and, on the one hand, the Fourier coefficients $a_n(f^*)$ and $b_n(f^*)$, and on the other hand the modulus of continuity $\omega(\delta,f)$. 
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È. A. Storozhenko. Necessary and sufficient conditions for the imbedding of some classes of functions. Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 388-400. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a8/

[1] Ulyanov P. L., “Vlozhenie nekotorykh klassov funktsii $H_p^\omega$”, Izv. AN SSSR. Ser. matem., 32 (1968), 649–686

[2] Ulyanov P. L., “Teoremy vlozheniya i sootnosheniya mezhdu nailuchshimi priblizheniyami (modulyami nepreryvnosti) v raznykh metrikakh”, Matem. sb., 81(123) (1970), 104–131

[3] Leindler L., “On embedding of classes $H^p$”, Acta Sci. Math., 31 (1970), 13–31 | MR | Zbl

[4] Timan M. F., “O nekotorykh teoremakh vlozhenii $L^p$-klassov funktsii”, Dokl. AN SSSR, 193 (1970), 1251–1254 | MR | Zbl

[5] Zigmund A., Trigonometricheskie ryady, t. 2, Mir, M., 1965 | MR

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

[7] Oskolkov K. I., Telyakovskii S. A., “K otsenkam P. L. Ulyanova dlya integralnykh modulei nepreryvnosti”, Izv. AN ArmSSR, Matematika, 6:5 (1971), 406–411 | MR