Geodesic
Widths of the Besov Classes $B_{p,\theta}^r(\mathbb T^d)$
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 656-665

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In this paper we obtain estimates of the orders of Kolmogorov widths of the Besov classes $B_{p,\theta}^r(\mathbb T^d)$ of periodic functions of several variables with dominant mixed derivative (defined in the sense of Weyl) in the space $L_q$, $r\in\mathbb R^d$, $1$, $0\theta\le\infty$. The proposed approach to calculating widths can also be used for finding the widths of the Sobolev classes $W_p^r(\mathbb T^d)$ (by embedding them in the Besov classes $B_{p,\theta}^r(\mathbb T^d)$) as well as for calculating some other widths (such as Alexandroff, linear, projective, and orthoprojective widths). 
@article{MZM_2001_69_5_a1,
     author = {\`E. M. Galeev},
     title = {Widths of the {Besov} {Classes} $B_{p,\theta}^r(\mathbb T^d)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {656--665},
     publisher = {mathdoc},
     volume = {69},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a1/}
}
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È. M. Galeev. Widths of the Besov Classes $B_{p,\theta}^r(\mathbb T^d)$. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 656-665. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a1/