Geodesic
Analogue of A. A. Markov's inequality for polynomials in two variables
Sbornik. Mathematics, Tome 199 (2008) no. 9, pp. 1409-1420 
V. I. Skalyga. Analogue of A. A. Markov's inequality for polynomials in two variables. Sbornik. Mathematics, Tome 199 (2008) no. 9, pp. 1409-1420. http://geodesic.mathdoc.fr/item/SM_2008_199_9_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A sharp estimate is obtained for a partial derivative of any order of polynomials in two variables at points outside the unit ball in $l_2^2$ for polynomials normed on the Chebyshev grid of points of the unit ball in $l_1^2$. Bibliography: 8 titles.

[1] V. A. Markov, O funktsiyakh, naimenee uklonyayuschikhsya ot nulya v dannom promezhutke, Tip. Imp. AN, SPb, 1892 | Zbl

[2] A. A. Markov, “Ob odnom voprose D. I. Mendeleeva”, Zapiski Peterburgskoi Akademii Nauk, 62 (1889), 1–24

[3] S. A. Telyakovskij, “Research in the theory of approximation of functions at the Mathematical Institute of the Academy of Sciences”, Proc. Steklov Inst. Math., 182:1 (1990), 141–197 | MR | Zbl

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

[5] G. G. Magaril-Il'yaev, V. M. Tikhomirov, Convex analysis: theory and applications, Transl. Math. Monogr., 222, Amer. Math. Soc., Providence, RI, 2003 | MR | Zbl

[6] V. I. Skalyga, “Bounds for the derivatives of polynomials on centrally symmetric convex bodies”, Izv. Math., 69:3 (2005), 607–621 | DOI | MR | Zbl

[7] G. A. Muñoz, Y. Sarantopoulos, “Bernstein and Markov-type inequalities for polynomials on real Banach spaces”, Math. Proc. Cambridge Philos. Soc., 133:3 (2002), 515–530 | DOI | MR | Zbl

[8] V. I. Skalyga, “Sharpness conditions in multidimensional analogs of V. A. Markov's inequality”, Math. Notes, 80:5–6 (2006), 893–897 | DOI | MR | Zbl