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. 
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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/

[1] Zigmund A., Trigonometricheskie ryady, t. I, IL, M., 1965

[2] Dantser L., Gryunbaum B., Kli V., Teorema Khelli, Mir, M., 1968

[3] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR

[4] Veil A., Integrirovanie v topologicheskikh gruppakh i ego primeneniya, IL, M., 1950

[5] Tikhomirov V. M., “Poperechniki mnozhestv v funktsionalnykh prostranstvakh i teoriya priblizhenii”, Uspekhi matem. nauk, XV:3 (1960), 81–120

[6] Sidelnikov V. M., “Novye otsenki dlya plotneishei upakovki sharov v $n$-mernom evklidovom prostranstve”, Matem. sb., 95(137) (1974), 148–158 | MR

[7] Kashin B. S., “Poryadki poperechnikov nekotorykh klassov gladkikh funktsii”, Uspekhi matem. nauk, 32:1 (1977), 191–192 | MR | Zbl

[8] Kolmogoroff A., “Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse”, Ann. Math., 37 (1936), 107–111 | DOI | MR

[9] Stechkin S. B., “O nailuchshikh priblizheniyakh zadannykh klassov funktsii lyubymi polinomami”, Uspekhi matem. nauk, IX:1 (1954), 133–134

[10] Babadzhanov S. B., Tikhomirov V. M., “O poperechnikakh odnogo klassa v prostranstve $L^p$”, Izv. AN Uzb. SSR. Ser. fiz.-matem., 2 (1967), 24–30 | Zbl

[11] Tikhomirov V. M., Doktorskaya dissertatsiya, M., 1969

[12] Makovoz Yu. I., “Ob odnom prieme otsenki snizu poperechnikov mnozhestv v banakhovom prostranstve”, Matem. sb., 87(129):1 (1972), 136–146 | MR | Zbl

[13] Ismagilov R. S., “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, Uspekhi matem. nauk, XXIX:3 (1974), 161–178 | MR

[14] Gluskin E. D., “Ob odnoi zadache o poperechnikakh”, Dokl. AN SSSR, 219:3 (1974), 527–530 | MR | Zbl

[15] Maiorov V. E., “Diskretizatsiya zadachi o poperechnikakh”, Uspekhi matem. nauk, XXX:6 (1975), 179–180 | MR

[16] Kashin B. S., “O poperechnikakh oktaedrov”, Uspekhi matem. nauk, XXX:4 (1975), 251–252

[17] Kashin B. S., “O kolmogorovskikh poperechnikakh oktaedrov”, Dokl. AN SSSR, 214:5 (1974), 1024–1026 | Zbl

[18] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, 1950