Geodesic
Approximation of Sobolev Classes by Their Finite-Dimensional Sections
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 370-382

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We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes of periodic functions of a single variable with constraints in $L_\infty$ or $L_1$ on higher-order derivatives, we present the exact orders of such widths in the spaces $L_q$. 
@article{MZM_2002_72_3_a5,
     author = {V. N. Konovalov},
     title = {Approximation of {Sobolev} {Classes} by {Their} {Finite-Dimensional} {Sections}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {370--382},
     publisher = {mathdoc},
     volume = {72},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a5/}
}
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V. N. Konovalov. Approximation of Sobolev Classes by Their Finite-Dimensional Sections. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 370-382. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a5/