Geodesic
Diameters of classes of smooth functions
Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 741-764

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We describe the weak asymptotic behaviour of diameters of $n$-th order of the unit ball of $W_p^l H^\omega (I^d)$ in $L_q(I^d)$, where $I=(0,1)$, in dependence on $n$. Namely we consider the Kolmogorov diameter, the Gel'fand diameter, the linear diameter, the Aleksandrov diameter and the entropy diameter. 
@article{IM2_1995_59_4_a4,
     author = {S. N. Kudryavtsev},
     title = {Diameters of classes of smooth functions},
     journal = {Izvestiya. Mathematics },
     pages = {741--764},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a4/}
}
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S. N. Kudryavtsev. Diameters of classes of smooth functions. Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 741-764. http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a4/