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On the Estimation of Strong Means of Fourier Series

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Ukrainian Mathematical Journal Aims and scope

We study problem of (λ, φ) -strong summation of number series by the regular method λ with power summation of the function φ . The accumulated results are extended to the case of Fourier expansions in trigonometric functions f ϵ L p , p > 1 , where C is the set of 2π-periodic continuous functions. Some results are also obtained for the estimation of strong means of the method λ in L p , p > 1 , at the Lebesgue point x of the function f under certain additional conditions in the case where the function φ tends to infinity as u→ ∞ faster than the exponential function exp (βu) − 1, β > 0 .

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References

  1. G. H. Hardy and J. E. Littlewood, “Sur la serie de Fourier d`une function a carre summable,” Comput. Revs., 156, 1307–1309 (1913).

    MATH  Google Scholar 

  2. G. H. Hardy and J. E. Littlewood, “On the strong summability of Fourier series,” Proc. London Math. Soc., 26, 273–286 (1926).

    MathSciNet  Google Scholar 

  3. L. Leindler, Strong Approximation by Fourier Series, Akadémiai Kiadó, Budapest (1985).

    MATH  Google Scholar 

  4. R. A. Lasuriya, Strong Summability of Fourier Series and Approximation of Functions [in Russian], Abkhazskii Gos. Univ., Sukhum (2010).

    Google Scholar 

  5. V. Totik, “On the strong approximation of Fourier series,” Acta Math. Acad. Sci. Hung., 35, 83–130 (1980).

    Article  MathSciNet  Google Scholar 

  6. L. D. Gogoladze, On Summation of Multiple Trigonometric Series and Conjugate Functions [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Tbilisi (1984).

  7. N. L. Pachulia, “Points of strong summability of Fourier series,” Ukr. Mat. Zh., 46, No. 12, 1955–1964 (1994); English translation: Ukr. Math. J., 46, No. 12, 1836–1847 (1994).

  8. G. Alexits, Convergence Problems of Orthogonal Series, Akadémiai Kiadó, Budapest (1961).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Abkhazia State University, Sukhumi, Abkhazia

    N. L. Pachulia

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  1. N. L. Pachulia
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 809–819, June, 2015.

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Pachulia, N.L. On the Estimation of Strong Means of Fourier Series. Ukr Math J 67, 916–927 (2015). https://doi.org/10.1007/s11253-015-1122-0

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  • DOI: https://doi.org/10.1007/s11253-015-1122-0

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