Ukrainian Mathematical Journal

, Volume 50, Issue 9, pp 1473–1477 | Cite as

On some inequalities for polynomials

  • M. F. Timan
Brief Communications


We prove the equivalence between analogs of the Paley and Nikol’skii inequalities for any orthonormal system of functions and for almost periodic polynomials with arbitrary spectrum.


Entire Function Periodic Function Differentiable Function Trigonometric Series Orthonormal System 
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    A. Zygmund, Trigonometric Series [Russian translation], Vol. 2, Mir, Moscow (1965).zbMATHGoogle Scholar
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    M. F. Timan, “On one property of orthonormal systems satisfying the Nikol’skii inequality/’ in: Proceedings of the International Conference on the Theory of Approximation of Functions [in Russian], Nauka, Moscow, pp. 356–358.Google Scholar
  3. 3.
    S. M. Nikol’skii, “Inequalities for entire functions of finite degree and their application in the theory of differentiable functions of many variables,” Tr. Mat. Inst. Steklova, 38, 244–278 (1958).Google Scholar
  4. 4.
    B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhizdat, Moscow-Leningrad (1947).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • M. F. Timan
    • 1
  1. 1.Dnepropetrovsk Agricultural UniversityDnepropetrovsk

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