Geodesic
The best approximation of classes $W_1^r(I^s)$ in the space $L_\infty(I^s)$
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 699-706.

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A method is proposed which enables us to obtain the best upper bounds for the $n$-diameters of multidmensional Sobolev classes $W_1^r(I^s)$ in the metric of $L_\infty(I^s)$. 
@article{MZM_1976_19_5_a4,
     author = {V. E. Maiorov},
     title = {The best approximation of classes $W_1^r(I^s)$ in the space $L_\infty(I^s)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {699--706},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a4/}
}
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V. E. Maiorov. The best approximation of classes $W_1^r(I^s)$ in the space $L_\infty(I^s)$. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 699-706. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a4/