A Bernstein type inequality for smooth splines
Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 4, pp. 31-41.

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In this paper we present a new Bernstein type inequality for smooth splines with non-fixed nodes.
Keywords: approximation theory, Bernstein inequality, splines.
Mots-clés : diadic spaces
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I. P. Irodova. A Bernstein type inequality for smooth splines. Modelirovanie i analiz informacionnyh sistem, Tome 15 (2008) no. 4, pp. 31-41. http://geodesic.mathdoc.fr/item/MAIS_2008_15_4_a3/

[1] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[2] I. P. Irodova, “Obobschenie neravenstva Marsho”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, Yaroslavl, 1984, 64–70

[3] I. P. Irodova, “O svoistvakh shkaly prostranstv $B_p^{\lambda\theta}$ pri $0

1$”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, Yaroslavl, 1982, 86–99

[4] R. A. Devore, V. A. Popov, “Interpolation of Besov Spaces”, Trans. Amer. Math. Soc., 305 (1988), 397–414 | DOI | MR | Zbl

[5] Yu. A. Brudnyi, I. P. Irodova, “Nelineinaya splain-approksimatsiya i $B$-prostranstva”, Algebra i analiz, 4:4 (1992), 45–79 | MR

[6] R. A. Devore, B. Jawerth, V. A. Popov, “Compression of wavelet decompositions”, Amer. J. Math., 114 (1992), 737–785 | DOI | MR | Zbl

[7] Rong-Qing Jia, “A Bernstein-Type Inequality Associated with Wavelet Decomposition”, Constr. Approx., 9 (1993), 299–318 | DOI | MR | Zbl

[8] R. A. Devore, P. P. Petruschev, X. M. Yu, “Nonlinear wavelet approximation in the space $C(R^d)$”, Progress in Approximation Theory (Tampa, FL 1990), Springer Ser. Comput. Math., 19, Springer, New York, 1992, 261–283 | MR | Zbl

[9] I. P. Irodova, “Diadicheskie prostranstva Besova”, Algebra i analiz, 12:3 (2000), 40–80 | MR

[10] Yu. A. Brudnyi, M. I. Gansburg, “Ob odnoi ekstremalnoi zadache dlya mnogochlenov $n$ peremennykh”, Izv. AN SSSR — Ser. mat., 37:2 (1973), 344–355 | MR

[11] Yu. A. Brudnyi, “Prostranstva, opredelyaemye s pomoschyu lokalnykh priblizhenii”, Tr. MMO, 24, 1971, 69–132 | MR

[12] E. A. Storozhenko, P. Osvald, “Teoremy Dzheksona v prostranstvakh $L_p$, $0

1$”, Sib. mat. zhurn., 19:4 (1978), 630–639

[13] I. P. Irodova, “O diadicheskikh prostranstvakh Nikolskogo — Besova i ikh svyazi s klassicheskimi prostranstvami”, Mat. zametki, 83:5 (2008), 683–695 | MR

[14] I. P. Irodova, “Diadicheskie proizvodnye i ikh svoistva”, Izvestiya Tulskogo Gosudarstvennogo universiteta. — Ceriya estestvennykh nauk, 1 (2008), 29–36, Tula

[15] F. John, L. Nirenberg, “On functions of bounded mean oscillation”, Comm. Pure Appl. Math., 14 (1961), 415–426 | DOI | MR | Zbl

[16] J. Peetre, G. Sparr, “Interpolation of normed Abelian groups”, Ann. Mat. Pura Appl., 92:4 (1972), 217–262 | MR | Zbl

[17] Yu. A. Brudnyi, “Adaptivnaya approksimatsiya funktsii s osobennostyami”, Tr. MMO, 55, 1994, 123–185 | MR

[18] J. Peetre, E. Svensson, “On the Generalized Hardy's inequality of Mcgehee, Pingo and Smith and the problem of interpolation between BMO and Besov Space”, Math. Scand., 54 (1984), 221–241 | MR | Zbl