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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 1, Pages 141–156 (Mi izv108)  

This article is cited in 3 scientific papers (total in 3 papers)

Analogues of the Markov and Bernstein inequalities for polynomials in Banach spaces

V. I. Skalyga


Abstract: We propose analogues of the inequalities of A. A. and V. A. Markov for algebraic polynomials on the cube in $\mathbb R^m$ in the $l_2^{(m)}$ and $l_1^{(m)}$ metrics, as well as for polynomials on closed bounded convex bodies in a Banach space and on centrally symmetric bodies of the same type. For the last two cases analogues of Bernstein's inequality are obtained.

DOI: https://doi.org/10.4213/im108

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English version:
Izvestiya: Mathematics, 1997, 61:1, 143–159

Bibliographic databases:

MSC: 41A17
Received: 30.06.1995

Citation: V. I. Skalyga, “Analogues of the Markov and Bernstein inequalities for polynomials in Banach spaces”, Izv. RAN. Ser. Mat., 61:1 (1997), 141–156; Izv. Math., 61:1 (1997), 143–159

Citation in format AMSBIB
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\paper Analogues of the Markov and Bernstein inequalities for polynomials in Banach spaces
\jour Izv. RAN. Ser. Mat.
\yr 1997
\vol 61
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\pages 141--156
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\pages 143--159
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  • https://doi.org/10.4213/im108
  • http://mi.mathnet.ru/eng/izv/v61/i1/p141

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Skalyga, “Multidimensional analogues of the Markov and Bernstein inequalities”, Izv. Math., 65:6 (2001), 1197–1241  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. 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  scopus
    3. 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  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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