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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 2, Pages 169–192 (Mi izv179)  

This article is cited in 6 scientific papers (total in 6 papers)

Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spaces

V. I. Skalyga


Abstract: 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.

DOI: https://doi.org/10.4213/im179

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English version:
Izvestiya: Mathematics, 1998, 62:2, 375–397

Bibliographic databases:

MSC: 41A17, 26D05
Received: 18.06.1996

Citation: V. I. Skalyga, “Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spaces”, Izv. RAN. Ser. Mat., 62:2 (1998), 169–192; Izv. Math., 62:2 (1998), 375–397

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Skalyga, “Analogs of the Markov and Schaeffer–Duffin inequalities for convex bodies”, Math. Notes, 68:1 (2000), 130–134  mathnet  crossref  mathscinet  zmath  isi
    2. V. I. Skalyga, “Multidimensional analogues of the Markov and Bernstein inequalities”, Izv. Math., 65:6 (2001), 1197–1241  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. Munoz G.A., Sarantopoulos Y., “Bernstein and Markov-type inequalities for polynomials on real Banach spaces”, Mathematical Proceedings of the Cambridge Philosophical Society, 133:Part 3 (2002), 515–530  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Revesz S.G., Sarantopoulos Y., “The generalized Minkowski functional with applications in approximation theory”, Journal of Convex Analysis, 11:2 (2004), 303–334  mathscinet  zmath  isi
    5. V. I. Skalyga, “Bounds for the derivatives of polynomials on centrally symmetric convex bodies”, Izv. Math., 69:3 (2005), 607–621  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Munoz-Fernandez G.A., Sanchez V.M., Seoane-Sepulveda J.B., “L-P-Analogues of Bernstein and Markov Inequalities”, Mathematical Inequalities & Applications, 14:1 (2011), 135–145  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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