Geodesic
Approximation of Classes of Periodic Functions in Several Variables
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 109-121.

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We study the approximation of the classes $B_{p,\theta }^r$ and $W_{p,\alpha }^r$ of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums. 
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A. S. Romanyuk. Approximation of Classes of Periodic Functions in Several Variables. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a9/

[1] Temlyakov V. N., Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi, Tr. MIAN, 178, Nauka, M., 1986 | MR | Zbl

[2] Kashin B. S., Temlyakov V. N., “O nailuchshikh $m$-chlennykh priblizheniyakh i entropii mnozhestv v prostranstve $L_1$”, Matem. zametki, 56:5 (1994), 57–86 | MR | Zbl

[3] Lizorkin P. I., Nikolskii S. M., “Prostranstva funktsii smeshannoi gladkosti s dekompozitsionnoi tochki zreniya”, Tr. MIAN, 187, Nauka, M., 1989, 143–161 | MR

[4] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969

[5] Belinskii E. S., “Priblizhenie plavayuschei sistemoi eksponent na klassakh periodicheskikh funktsii s ogranichennoi smeshannoi proizvodnoi”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, YaGU, Yaroslavl, 1988, 16–33 | MR

[6] Romanyuk A. S., “Priblizhenie klassov Besova periodicheskikh funktsii mnogikh peremennykh v prostranstve $L_q$”, Ukr. matem. zh., 43:10 (1991), 1398–1408 | MR | Zbl

[7] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987

[8] Galeev E. M., “Poryadkovye otsenki proizvodnykh periodicheskogo mnogomernogo $\alpha$-yadra Dirikhle v smeshannoi norme”, Matem. sb., 117:1 (1982), 32–43 | MR | Zbl

[9] Galeev E. M., “Priblizhenie klassov periodicheskikh funktsii neskolkikh peremennykh yadernymi operatorami”, Matem. zametki, 47:3 (1990), 32–41 | MR | Zbl

[10] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | Zbl