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Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 6, Pages 9–19 (Mi ivm8900)  

This article is cited in 4 scientific papers (total in 4 papers)

Estimates for $L_p$-norms of simple partial fractions

V. I. Danchenko, A. E. Dodonov

Chair of Functional Analysis and its Applications, Vladimir State University, 87 Gorky str., Vladimir, 600000 Russia

Abstract: We obtain estimates for $L_p$-norms of simple partial fractions in terms of their $L_r$-norms on limited and unlimited segments of the real axis for different $p>1$ and $r>1$ (S. M. Nikolskii type inequalities). We adduce examples and remarks about sharpness of these inequalities and sphere of their application.

Keywords: simple partial fractions, $L_p$-norms, estimates for derivatives of simple partial fractions.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:6, 6–15

UDC: 517.538+517.444
Received: 17.12.2012

Citation: V. I. Danchenko, A. E. Dodonov, “Estimates for $L_p$-norms of simple partial fractions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 6, 9–19; Russian Math. (Iz. VUZ), 58:6 (2014), 6–15

Citation in format AMSBIB
\Bibitem{DanDod14}
\by V.~I.~Danchenko, A.~E.~Dodonov
\paper Estimates for $L_p$-norms of simple partial fractions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 6
\pages 9--19
\mathnet{http://mi.mathnet.ru/ivm8900}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 6
\pages 6--15
\crossref{https://doi.org/10.3103/S1066369X14060024}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84900871294}


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    This publication is cited in the following articles:
    1. Chunaev P., “Least Deviation of Logarithmic Derivatives of Algebraic Polynomials From Zero”, J. Approx. Theory, 185 (2014), 98–106  crossref  mathscinet  zmath  isi  elib
    2. V. I. Danchenko, L. A. Semin, “Sharp quadrature formulas and inequalities between various metrics for rational functions”, Siberian Math. J., 57:2 (2016), 218–229  mathnet  crossref  crossref  mathscinet  isi  elib
    3. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    4. P. Chunaev, V. Danchenko, “Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions”, J. Approx. Theory, 228 (2018), 1–20  crossref  mathscinet  zmath  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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