Geodesic
Estimates for the widths of classes of periodic functions of several variables~--~I
Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 11-26

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We establish estimates sharp in order for the Kolmogorov and linear widths of the classes $\mathrm{B}^{s\,m}_{p\,q}(\,\mathbb{T}^k)$ and $\mathrm{L}^{s\,m}_{p\,q}(\,\mathbb{T}^k)$ of Nikol'skii–Besov, Lizorkin–Triebel types respectively, in the space $L_r(\mathbb{T}^k)$ for a certain range of the parameters $s,p,q,r$, and $m$. 
@article{EMJ_2010_1_3_a1,
     author = {D. B. Bazarkhanov},
     title = {Estimates for the widths of classes of periodic functions of several {variables~--~I}},
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     publisher = {mathdoc},
     volume = {1},
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     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a1/}
}
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D. B. Bazarkhanov. Estimates for the widths of classes of periodic functions of several variables~--~I. Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 11-26. http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a1/