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Estimates for L p -norms of simple partial fractions

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Abstract

We obtain estimates for L p -norms of simple partial fractions in terms of their L r -norms on bounded and unbounded segments of the real axis for various p > 1 and r > 1 (S. M. Nikolskii type inequalities). We adduce examples and remarks concerning sharpness of the inequalities and area of their application.

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Authors and Affiliations

  1. Vladimir State University, ul. Gor’kogo 87, Vladimir, 600000, Russia

    V. I. Danchenko & A. E. Dodonov

Authors
  1. V. I. Danchenko
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  2. A. E. Dodonov
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Correspondence to V. I. Danchenko.

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Original Russian Text © V.I. Danchenko, A.E. Dodonov, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 6, pp. 9–19.

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Danchenko, V.I., Dodonov, A.E. Estimates for L p -norms of simple partial fractions. Russ Math. 58, 6–15 (2014). https://doi.org/10.3103/S1066369X14060024

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  • DOI: https://doi.org/10.3103/S1066369X14060024

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