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Izv. Vyssh. Uchebn. Zaved. Mat., 2012, Number 4, Pages 33–45 (Mi ivm8592)  

This article is cited in 5 scientific papers (total in 5 papers)

Integral bounds for simple partial fractions

I. R. Kayumov

Chebotaryov Research Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: For $p\ge2$ we obtain bounds of $L_p$-norms of the Fourier transform of real parts of simple partial fractions. For even $p$ our estimate is sharp. We also prove a new inequality for $L_p$-norms of simple partial fractions which in some cases is stronger than the corresponding inequality obtained by V. Yu. Protasov.

Keywords: simple partial fractions, Fourier transform, Hausdorff–Young inequality, Dirichlet series.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:4, 27–37

Bibliographic databases:

UDC: 517.538+517.444
Received: 25.03.2011

Citation: I. R. Kayumov, “Integral bounds for simple partial fractions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 4, 33–45; Russian Math. (Iz. VUZ), 56:4 (2012), 27–37

Citation in format AMSBIB
\Bibitem{Kay12}
\by I.~R.~Kayumov
\paper Integral bounds for simple partial fractions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 4
\pages 33--45
\mathnet{http://mi.mathnet.ru/ivm8592}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076539}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 4
\pages 27--37
\crossref{https://doi.org/10.3103/S1066369X12040044}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862726918}


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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. A. V. Kayumova, “Skhodimost ryadov prostykh drobei v $L_p(\mathbb R)$”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2012, 208–213  mathnet
    2. V. I. Danchenko, A. E. Dodonov, “Estimates for $L_p$-norms of simple partial fractions”, Russian Math. (Iz. VUZ), 58:6 (2014), 6–15  mathnet  crossref
    3. 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
    4. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    5. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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