Acta Mathematica Hungarica

, Volume 115, Issue 1–2, pp 79–100

On the convergence of generalized Cesàro means of trigonometric Fourier series. II

  • T. Akhobadze
Article

Abstract

The behavior of generalized Cesàro (C, αn)-means (αn ∈ (−1,0)) of trigonometric Fourier series of Hω classes in the space of continuous functions is studied. The sharpness of the results obtained is shown.

Key words and phrases

trigonometric system Fourier series Cesàro means Hw classes 

2000 Mathematics Subject Classification

42A24 

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References

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    A. Zygmund, Sur la’sommabilité des séries de Fourier des functions vérifiant la condition de Lipschitz, Bull. de I’Acad., Polon. (1925), 1–9.Google Scholar
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    T. Akhobadze, On the uniform convergence and (C, α)-summability of trigonometric Fourier series, Bull. Georgian Acad. Sci., 128 (1987), 249–252 (in Russian).MATHMathSciNetGoogle Scholar
  3. [3]
    A. Zygmund, Trigonometric Series, Cambridge University Press, Vol. 1 (1959).Google Scholar
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    T. Akhobadze, On the convergence of generalized Cesáro means of trigonometric Fourier series. I, Acta Math. Hungar. (to appear).Google Scholar
  5. [5]
    L. Zhizhiashvili, Conjugate Functions and Trigonometric Series, Tbilisi University Press (1969) (in Russian).Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest 2007

Authors and Affiliations

  • T. Akhobadze
    • 1
  1. 1.Institute of MathematicsIV. Javakhishvili Tbilisi State UniversityTbilisiGeorgia

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