Geodesic
Various widths of the class $H_p^r$ in the space~$L_q$
Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 73-87

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A method of reducing the computation of $n$-widths of compact sets of functions to the analogous problem for finite-dimensional compact sets is presented. Using this method the author obtains best possible (in the “power scale”) estimates for Kolmogorov, Aleksandrov and entropy $n$-widths of the class $H_p^r$ of functions $f(x)$, $x\in R^S$, that are $2\pi$-periodic in each variable, satisfy the inequality $$ \biggl\|\frac{\partial^{rs}}{\partial x_1^r\cdots\partial x_s^r}\biggr\|_{L_p}\leqslant1 $$ and have the property that any Fourier coefficients with at least one zero index must be equal to zero. Bibliography: 21 titles. 
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     author = {V. E. Maiorov},
     title = {Various widths of the class $H_p^r$ in the space~$L_q$},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a4/}
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V. E. Maiorov. Various widths of the class $H_p^r$ in the space~$L_q$. Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 73-87. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a4/