Geodesic
Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions
Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 285-322

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The author investigates questions of the approximation of functions of several variables with a bounded mixed derivative or difference. He finds the orders of the Kolmogorov widths and of other widths of these classes. He obtains embedding theorems and estimates for the best approximations by trigonometric polynomials to functions in these classes. Bibliography: 32 titles. 
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     author = {V. N. Temlyakov},
     title = {Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions},
     journal = {Izvestiya. Mathematics },
     pages = {285--322},
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     volume = {27},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a5/}
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V. N. Temlyakov. Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions. Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 285-322. http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a5/