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The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval. / Glazyrina, P. Yu.
In: Mathematical Notes, Vol. 84, No. 1-2, 01.08.2008, p. 3-21.

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Harvard

Glazyrina, PY 2008, 'The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval', Mathematical Notes, vol. 84, no. 1-2, pp. 3-21. https://doi.org/10.1134/S0001434608070018

APA

Glazyrina, P. Y. (2008). The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval. Mathematical Notes, 84(1-2), 3-21. https://doi.org/10.1134/S0001434608070018

Vancouver

Glazyrina PY. The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval. Mathematical Notes. 2008 Aug 1;84(1-2):3-21. doi: 10.1134/S0001434608070018

Author

Glazyrina, P. Yu. / The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval. In: Mathematical Notes. 2008 ; Vol. 84, No. 1-2. pp. 3-21.

BibTeX

@article{a57dd2dc16b44b5d97df05712d9e1b73,
title = "The sharp Markov-Nikol{\textquoteright}skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval",
abstract = "In this paper, an inequality between the L q -mean of the kth derivative of an algebraic polynomial of degree n ≥ 1 and the L 0-mean of the polynomial on a closed interval is obtained. Earlier, the author obtained the best constant in this inequality for k = 0, q ∈ [0,∞] and 1 ≤ k ≤ n, q ∈ {0} ∪ [1,∞]. Here a newmethod for finding the best constant for all 0 ≤ k ≤ n, q ∈ [0,∞], and, in particular, for the case 1 ≤ k ≤ n, q ∈ (0, 1), which has not been studied before is proposed. We find the order of growth of the best constant with respect to n as n → ∞ for fixed k and q.",
author = "Glazyrina, {P. Yu.}",
note = "The author wishes to express gratitude to Professor V. V. Arestov for the statement of the problem and constant interest in the paper. This work was supported by the Russian Foundation for Basic Research (grant no. 05-01-00233) and the program “Leading Scientific Schools” (grant no. NSh-5120.2006.1).",
year = "2008",
month = aug,
day = "1",
doi = "10.1134/S0001434608070018",
language = "English",
volume = "84",
pages = "3--21",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Kluwer Academic/Plenum Publishers",
number = "1-2",

}

RIS

TY - JOUR

T1 - The sharp Markov-Nikol’skii inequality for algebraic polynomials in the spaces L q and L 0 on a closed interval

AU - Glazyrina, P. Yu.

N1 - The author wishes to express gratitude to Professor V. V. Arestov for the statement of the problem and constant interest in the paper. This work was supported by the Russian Foundation for Basic Research (grant no. 05-01-00233) and the program “Leading Scientific Schools” (grant no. NSh-5120.2006.1).

PY - 2008/8/1

Y1 - 2008/8/1

N2 - In this paper, an inequality between the L q -mean of the kth derivative of an algebraic polynomial of degree n ≥ 1 and the L 0-mean of the polynomial on a closed interval is obtained. Earlier, the author obtained the best constant in this inequality for k = 0, q ∈ [0,∞] and 1 ≤ k ≤ n, q ∈ {0} ∪ [1,∞]. Here a newmethod for finding the best constant for all 0 ≤ k ≤ n, q ∈ [0,∞], and, in particular, for the case 1 ≤ k ≤ n, q ∈ (0, 1), which has not been studied before is proposed. We find the order of growth of the best constant with respect to n as n → ∞ for fixed k and q.

AB - In this paper, an inequality between the L q -mean of the kth derivative of an algebraic polynomial of degree n ≥ 1 and the L 0-mean of the polynomial on a closed interval is obtained. Earlier, the author obtained the best constant in this inequality for k = 0, q ∈ [0,∞] and 1 ≤ k ≤ n, q ∈ {0} ∪ [1,∞]. Here a newmethod for finding the best constant for all 0 ≤ k ≤ n, q ∈ [0,∞], and, in particular, for the case 1 ≤ k ≤ n, q ∈ (0, 1), which has not been studied before is proposed. We find the order of growth of the best constant with respect to n as n → ∞ for fixed k and q.

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U2 - 10.1134/S0001434608070018

DO - 10.1134/S0001434608070018

M3 - Article

VL - 84

SP - 3

EP - 21

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -

ID: 38708537