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

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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. 
@article{IM2_1983_20_3_a8,
     author = {A. I. Stepanets},
     title = {Suprema of {Fourier} coefficients on classes of continuous and differentiable functions of several variables},
     journal = {Izvestiya. Mathematics },
     pages = {611--624},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a8/}
}
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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/