Geodesic
Diameters of some finite-dimensional sets and classes of smooth functions
Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 317-333

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Estimates of the diameters of certain sets in the Banach spaces $L^q(0,1)$ and $l_q^n$ are given; in particular, the orders of the diameters $d_n(W_p^r,L^q)$, $p$, $r>1$, are completely determined. Bibliography: 18 titles. 
@article{IM2_1977_11_2_a5,
     author = {B. S. Kashin},
     title = {Diameters of some finite-dimensional sets and classes of smooth functions},
     journal = {Izvestiya. Mathematics },
     pages = {317--333},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a5/}
}
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B. S. Kashin. Diameters of some finite-dimensional sets and classes of smooth functions. Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 317-333. http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a5/