Geodesic
On embedding in classes of continuous functions of several variables
Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 377-388 
V. I. Kolyada. On embedding in classes of continuous functions of several variables. Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 377-388. http://geodesic.mathdoc.fr/item/SM_1976_28_3_a7/
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     author = {V. I. Kolyada},
     title = {On embedding in classes of continuous functions of several variables},
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     volume = {28},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_3_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

P. L. Ul'yanov (RZhMat., 1968, 5B120) has found necessary and sufficient conditions for each function of the class $H_p^\omega$ (where $1, and $\omega$ is a modulus of continuity) to be equivalent to a continuous function on $[0,1]$ or to a function of the class $\operatorname{Lip}\alpha$. Ul'yanov's research for functions of one variable was continued by V. A. Andrienko (RZhMat., 1969, 2B110). In the present paper, analogous questions for functions of several variables are considered. Bibliography: 6 titles.

[1] P. L. Ulyanov, “Ob absolyutnoi i ravnomernoi skhodimosti ryadov Fure”, Matem. sb., 72(114) (1967), 193–224

[2] N. Temirgaliev, “O svyazi teorem vlozheniya s ravnomernoi skhodimostyu kratnykh ryadov Fure”, Matem. zametki, 12:2 (1972), 139–148 | MR | Zbl

[3] V. A. Andrienko, “Vlozhenie nekotorykh klassov funktsii”, Izv. AN SSSR, seriya matem., 31 (1967), 1311–1326 | MR | Zbl

[4] V. I. Kolyada, “O vlozhenii v klassy $\varphi(L)$”, Izv. AN SSSR, seriya matem., 39 (1975), 418–437 | Zbl

[5] V. I. Kolyada, “O vlozhenii nekotorykh klassov funktsii mnogikh peremennykh”, Sib. matem. zh., XI:4 (1973), 766–790

[6] A. Zigmund, Trigonometricheskie ryady, t. 2, izd-vo «Mir», Moskva, 1965 | MR