Abstract
We investigate sine and cosine series such that their coefficients tend to zero and some subsequences of the coefficients have bounded variation.
Similar content being viewed by others
References
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].
Zygmund, A. Trigonometric Series (Cambridge University Press, Cambridge, 1959; Mir, Moscow, 1965), Vol. 1.
Barim N. A Treatise on Trigonometric Series (Pergamon Press, Oxford, New York, 1964).
Ul’yanov, P. L. “Integrals of Cauchy Type”, Trudy Mat. Inst. Steklov, Acad. Sci. USSR, Moscow 60, 262–281 (1961) [in Russian].
Simonov, B. V. “Trigonometric Series in the Orlicz–Lorentz Spaces”, RussianMathematics 51, No. 6, 61–74 (2007).
Simonov, B. V. “Sine and Cosine Series in Lϕ Classes”, RussianMathematics 57, No. 10, 19–36 (2013).
Young, W. H. “On the Fourier Series of Bounded Functions”, Proc. London Math. Soc. 12, 41–70 (1913).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © B.V. Simonov, I.E. Simonova, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 4, pp. 50–58.
About this article
Cite this article
Simonov, B.V., Simonova, I.E. A-integrability of sums of trigonometric series. Russ Math. 61, 41–48 (2017). https://doi.org/10.3103/S1066369X17040077
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X17040077