Geodesic
Bernstein width of a~class of functions of finite smoothness
Sbornik. Mathematics, Tome 190 (1999) no. 4, pp. 539-560

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A weak asymptotic formula is obtained for the Bernstein $n$-width in the space $L_q(I^d)$ of the class $F_p^{l,\omega }(I^d)$ of functions on the cube $I^d$ such that their generalized partial derivatives up to order $l$ belong to $L_p(I^d)$ and the moduli of continuity in the space $L_p(I^d)$ of all their derivatives of order $l$ are majorized by a fixed modulus of continuity $\omega$. 
@article{SM_1999_190_4_a3,
     author = {S. N. Kudryavtsev},
     title = {Bernstein width of a~class of functions of finite smoothness},
     journal = {Sbornik. Mathematics},
     pages = {539--560},
     publisher = {mathdoc},
     volume = {190},
     number = {4},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_4_a3/}
}
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S. N. Kudryavtsev. Bernstein width of a~class of functions of finite smoothness. Sbornik. Mathematics, Tome 190 (1999) no. 4, pp. 539-560. http://geodesic.mathdoc.fr/item/SM_1999_190_4_a3/