Bounds for the derivatives of polynomials on centrally symmetric
Izvestiya. Mathematics , Tome 69 (2005) no. 3, pp. 607-621.

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Exact multidimensional analogues of V. A. Markov's inequality are found for the derivatives of polynomials on centrally symmetric bodies.
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V. I. Skalyga. Bounds for the derivatives of polynomials on centrally symmetric. Izvestiya. Mathematics , Tome 69 (2005) no. 3, pp. 607-621. http://geodesic.mathdoc.fr/item/IM2_2005_69_3_a4/

[1] Markov A. A., Ob odnom voprose D. I. Mendeleeva. Izbrannye trudy, GITTL, M.–L., 1948

[2] Markov V. A., O funktsiyakh, naimenee uklonyayuschikhsya ot nulya v dannom promezhutke, Izd-vo Imp. AN, SPb., 1892

[3] Schaeffer A. C., Duffin R. J., “On some inequalities of S. Bernstein and W. Markov for derivatives of polynomials”, Bull. Amer. Math. Soc., 44:4 (1938), 289–297 | DOI | Zbl

[4] Telyakovskii S. A., “O rabotakh po teorii priblizheniya funktsii, vypolnennykh v MIAN”, Tr. MIAN SSSR, 182, Nauka, M., 1988, 128–179 | MR

[5] Andrianov A. V., “On some open problems for algebraic polynomials on bounded convex sets”, EAST J. Approx., 5:1 (1999), 117–123 | MR | Zbl

[6] Kellogg O. D., “On bounded polynomials on several variables”, Math. Zeit., 27:1 (1928), 55–64 | DOI | MR

[7] Sarantopoulos Y., “Bounds on derivatives of polynomials on Banach spaces”, Math. Proc. Camb. Phil. Soc., 110 (1991), 307–312 | DOI | MR | Zbl

[8] Subbotin Yu. N., Vasilev Yu. S., “Neravenstva Markova v $\mathbb R^m$, ne uluchshaemye na klasse vsekh vypuklykh kompaktnykh tel”, Dokl. RAN, 360:6 (1998), 734–735 | MR | Zbl

[9] Skalyga V. I., “Otsenki proizvodnykh polinomov na vypuklykh telakh”, Tr. MIAN, 218, Nauka, M., 1997, 374–384 | MR | Zbl

[10] Skalyga V. I., “Mnogomernye analogi neravenstv V. A. Markova i S. N. Bernshteina.”, Izv. RAN. Ser. matem., 65:6 (2001), 129–172 | MR | Zbl

[11] Skalyga V. I., “Analogi neravenstv Markovykh i Bernshteina na vypuklykh telakh v banakhovykh prostranstvakh”, Izv. RAN. Ser. matem., 62:2 (1998), 169–192 | MR | Zbl

[12] Taylor A. E., “Additions to the theory of polynomials in normed spaces”, Tohoku Math. J., 44 (1938), 302–318 | Zbl

[13] Banach S., “Über homogone Polynome in $L^2$”, Studia Math., 7 (1938), 36–44 | Zbl

[14] Harris L. A., “Bounds on the derivatives of holomorphic functions of vectors”, Analyse Fonctionnele et Applications, ed. L. Nachbin, Hermann, Paris, 1975, 145–163 | MR

[15] Andrianov A. V., “Analogi neravenstv A. Markova i S. Bernshteina dlya mnogochlenov v banakhovykh prostranstvakh”, Matem. zametki, 52:5 (1992), 13–21 | MR | Zbl

[16] Skalyga V. I., “Analogi neravenstv V. Markova, A. Sheffera i R. Daffina na vypuklykh telakh”, Matem. zametki, 68:1 (2000), 146–150 | MR | Zbl

[17] Miñoz G. A., Sarantopoulos Y., “Bernstein and Markov-type inequalities for polynomials on a real Banach space”, Math. Proc. Camb. Phil. Soc., 133 (2002), 515–530 | DOI | MR