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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 4, Pages 240–248 (Mi timm882)  

This article is cited in 1 scientific paper (total in 1 paper)

On S. M. Nikol'skii type inequalities between different metrics

J. I. Mamedkhanov

Baku State University

Abstract: The paper is devoted to the derivation of analogs of S. M. Nikol'skii type inequalities for algebraic polynomials in weighted spaces and for rather general classes of curves in the complex plane. We announced similar inequalities for less general classes of curves and simpler weight functions earlier and in joint papers with I. I. Ibragimov. The order optimality of the inequalities follows from the obtained corollaries, which hold for a closed interval of the real line.
Note that similar inequalities on the real line were obtained by S. M. Nikol'skii, N. K. Bari, I. I. Ibragimov, S. B. Stechkin, A. F. Timan, V. V. Arestov, and others.

Keywords: S. M. Nikol'skii type inequalities, complex plane, algebraic polynomial, quasiconformal curves, conformal mapping, level curve, Salayev curves.

Full text: PDF file (178 kB)
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UDC: 517.5
Received: 17.03.2011

Citation: J. I. Mamedkhanov, “On S. M. Nikol'skii type inequalities between different metrics”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 240–248

Citation in format AMSBIB
\Bibitem{Mam12}
\by J.~I.~Mamedkhanov
\paper On S.\,M.~Nikol'skii type inequalities between different metrics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 4
\pages 240--248
\mathnet{http://mi.mathnet.ru/timm882}
\elib{http://elibrary.ru/item.asp?id=18126485}


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    This publication is cited in the following articles:
    1. Chunaev P. Danchenko V., “Quadrature Formulas With Variable Nodes and Jackson-Nikolskii Inequalities For Rational Functions”, J. Approx. Theory, 228 (2018), 1–20  crossref  mathscinet  zmath  isi  scopus
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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