Geodesic
On linear widths of Sobolev classes and chains of extremal subspaces
Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 361-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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The linear and trigonometric $n$-diameters of the class $\widetilde W^r_p$ in $L_q$ are calculated in this paper. For the linear diameter $\lambda_n$ it is proved that, when $p<2 and $r>\frac1p+\frac12$, $$ \lambda_n(\widetilde W^r_p,L_q)\asymp\begin{cases}n^{-r+\frac1p-\frac12},&\frac1p+\frac1q\leqslant1,\\n^{-r+\frac12-\frac1q},&\frac1p+\frac1q>1.\end{cases} $$ This formula, together with the known results for other $(p,q)$, finishes the solution of the problem of asymptotic computation of the linear diameters for the Sobolev classes in the one-dimensional periodic case when $r>\frac1p+\frac12$. Bibliography: 28 titles. 
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     author = {V. E. Maiorov},
     title = {On linear widths of {Sobolev} classes and chains of extremal subspaces},
     journal = {Sbornik. Mathematics},
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     volume = {41},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_41_3_a2/}
}
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V. E. Maiorov. On linear widths of Sobolev classes and chains of extremal subspaces. Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 361-382. http://geodesic.mathdoc.fr/item/SM_1982_41_3_a2/

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