Russian Mathematics

, Volume 61, Issue 4, pp 41–48 | Cite as

A-integrability of sums of trigonometric series



We investigate sine and cosine series such that their coefficients tend to zero and some subsequences of the coefficients have bounded variation.


A-integral series subsequence convergence almost everywhere 


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  1. 1.
    Ul’yanov, P. L. “Application of A-Integration to a Class of Trigonometric Series”, Mat. Sb. (N. S.) 35, No. 3, 469–490 (1954) [in Russian].MathSciNetMATHGoogle Scholar
  2. 2.
    Zygmund, A. Trigonometric Series (Cambridge University Press, Cambridge, 1959; Mir, Moscow, 1965), Vol. 1.MATHGoogle Scholar
  3. 3.
    Barim N. A Treatise on Trigonometric Series (Pergamon Press, Oxford, New York, 1964).Google Scholar
  4. 4.
    Ul’yanov, P. L. “Integrals of Cauchy Type”, Trudy Mat. Inst. Steklov, Acad. Sci. USSR, Moscow 60, 262–281 (1961) [in Russian].MathSciNetGoogle Scholar
  5. 5.
    Simonov, B. V. “Trigonometric Series in the Orlicz–Lorentz Spaces”, RussianMathematics 51, No. 6, 61–74 (2007).MathSciNetMATHGoogle Scholar
  6. 6.
    Simonov, B. V. “Sine and Cosine Series in Lϕ Classes”, RussianMathematics 57, No. 10, 19–36 (2013).MathSciNetMATHGoogle Scholar
  7. 7.
    Young, W. H. “On the Fourier Series of Bounded Functions”, Proc. London Math. Soc. 12, 41–70 (1913).MathSciNetCrossRefMATHGoogle Scholar

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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Volgograd State Technical UniversityVolgogradRussia

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