Analysis Mathematica

, Volume 34, Issue 1, pp 51–57 | Cite as

On an argument of Körner and Hardy’s inequality

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Abstract

We prove two probabilistic versions of Hardy’s inequality by using an argument suggested by Körner in [2].

Keywords

Unit Circle London Math Bounded Function Independent Random Variable Trigonometric Polynomial 
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Об одной идее Кернера и неравенстве Харди

Реэюме

На основе идеи Кернера, предлозенной в [2], в данной работе устанавливаются два вероятностных варианта неравенства Харди.

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References

  1. [1]
    J.-P. Kahane, Sur les polynômes á coefficients unimodulaires, Bull. London Math. Soc., 12(1980), 321–342.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    T. W. Körner, On a polynomial of Byrnes, Bull. London Math. Soc., 12(1980), 219–224.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    O. C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L 1 norm of exponential sums, Annals Math., 113(1981), 613–618.CrossRefMathSciNetGoogle Scholar
  4. [4]
    A. Rényi, Probability theory, North-Holland (Amstrdam, 1970).Google Scholar
  5. [5]
    B. Smith, Two trigonometric designs, ISNM 64 General Inequalities. 3, Birkhauser (Basel, 1983), 141–148.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsJordan UniversityAmmanJordan

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