Geodesic
Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spaces
Izvestiya. Mathematics, Tome 62 (1998) no. 2, pp. 375-397 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain analogues of the A. A. Markov and Bernstein inequalities for algebraic polynomials on convex bounded closed bodies in Banach spaces. For centrally symmetric bodies we establish an exact estimate in Markov's inequality, an estimate in Bernstein's inequality that is asymptotically exact for polynomials on the ball, and estimates for the norms of higher derivatives. 
@article{IM2_1998_62_2_a6,
     author = {V. I. Skalyga},
     title = {Analogues of the {Markov} and {Bernstein} inequalities on convex bodies in {Banach} spaces},
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     year = {1998},
     volume = {62},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a6/}
}
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V. I. Skalyga. Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spaces. Izvestiya. Mathematics, Tome 62 (1998) no. 2, pp. 375-397. http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a6/

[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, S.-Pb., 1892 | Zbl

[3] Bernshtein S. N., Sobranie sochinenii, T. 1, Izd-vo AN SSSR, M., 1952

[4] Bernshtein S. N., Sobranie sochinenii, T. 2, Izd-vo AN SSSR, M., 1954

[5] Kellogg O. D., “On bounded polynomials on several variables”, Math. Zeit., 27:1 (1927), 55–66 | DOI | MR

[6] Don R., “Wilhelmsen A. Markov Inequality in Several Dimensions”, J. of Approx. Theory, 11:3 (1974), 216–220 | DOI | MR | Zbl

[7] Pawlucki W., Plesniak W., “Markov's Inequality and $C^\infty$ Functions on Sets with Polynomial Cusps”, Math. Ann., 275 (1986), 467–480 | DOI | MR | Zbl

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

[9] Krasnoselskii M. A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966 | MR

[10] Kollatts L., Krabs V., Teoriya priblizhenii, Nauka, M., 1978 | MR

[11] Schaeffer A. C., Duffin R. I., “A refinement of an inequality of the brothers Markoff”, Trans. Amer. Math. Soc., 50:3 (1941), 517–522 | DOI | MR

[12] Bialas-Ciez L., Goetgheluck P., “Constants in Markov's inequality on convex sets”, EAST J. Approx., 1:3 (1995), 379–389 | MR | Zbl

[13] Baran M., “Markov inequality on sets with polynomial parametrization”, Ann. Polon. Math., LX:1 (1994) | MR