Geodesic
Suprema of Fourier coefficients on classes of continuous and differentiable functions of several variables
Izvestiya. Mathematics, Tome 20 (1983) no. 3, pp. 611-624 
A. I. Stepanets. Suprema of Fourier coefficients on classes of continuous and differentiable functions of several variables. Izvestiya. Mathematics, Tome 20 (1983) no. 3, pp. 611-624. http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a8/
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     author = {A. I. Stepanets},
     title = {Suprema of {Fourier} coefficients on classes of continuous and differentiable functions of several variables},
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     volume = {20},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Equalities that are multidimensional analogues of the familiar Lebesgue–Nikol'skii–Efimov relations are obtained for upper bounds of Fourier coefficients on classes of continuous and differentiable functions of several variables. Bibliography: 6 titles.

[1] Lebeg A., “Sur la representation triegonometrique approcheé des fonction satisfaisant à une condition de Lipschitz”, Bull. Math. de France, 39 (1910), 184–210

[2] Efimov A. V., “Priblizhenie nepreryvnykh periodicheskikh funktsii summami Fure”, Izv. AN SSSR. Ser. matem., 24:2 (1960), 243–296 | MR | Zbl

[3] Nikolskii S. M., “Ryad Fure funktsii s dannym modulem nepreryvnosti”, Dokl. AN SSSR, 52:3 (1946), 191–194

[4] Stepanets A. I., Priblizhenie summami Fure nepreryvnykh periodicheskikh funktsii mnogikh peremennykh, preprint IM-77-2, Kiev, 1977 | MR

[5] Stepanets V. I., “Otsenki otklonenii chastnykh summ Fure na klassakh nepreryvnykh periodicheskikh funktsii mnogikh peremennykh”, Izv. AN SSSR. Ser. matem., 44:5 (1980), 1150–1190 | MR | Zbl

[6] Ponomarenko V. G., O lineinykh protsessakh priblizheniya nepreryvnykh periodicheskikh funktsii dvukh peremennykh, avtoreferat kand. diss., Dnepropetrovsk, 1956