Skip to main content
SpringerLink
Log in

On L p-convergence of Cesàro means for Fourier series with monotonic coefficients

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

For sine and cosine Fourier serieswithmonotonic coefficients we study L p-convergence (1 < p < ∞) of their Cesàro means of a negative order.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Taberski, R. “On the Convergence of Singular Integrals”, Zesyty Naukowe Uniw. A.Mickewicza.Math. Fiz. Chem. 2, 33–51 (1960).

    MathSciNet  Google Scholar 

  2. Ul’yanov, P. L. “On Approximation of Functions”, Sib.Mat. Zhurn. 5, No. 2, 418–437 (1964).[in Russian].

    MATH  Google Scholar 

  3. Men’shov, D. E. “Application of Cesàro Summability Methods of Negative Order to Trigonometric Fourier Series of Summable and Square Summable Functions”, Mat. Sb.,N. Ser. 93, 494–511 (1974).[in Russian].

    Google Scholar 

  4. Kudryavtsev, A. I., Survillo, G. S. “A Criterion for L p-Summability of Fourier Series by Cesàro Methods of Negative Order”, Soviet Mathematics (Iz.VUZ) 34, No. 11, 57–61 (1990).

    MathSciNet  MATH  Google Scholar 

  5. Zhizhiashvili, L. V. “Convergence and Summability of Fourier Series”, MathematicalNotes 19, No. 6, 518–524 (1976).

    MATH  Google Scholar 

  6. Bari, N. K. Trigonometric Series (Moscow, Fizmatgiz, 1961) [in Russian].

    Google Scholar 

  7. Galoyan, L.N. “On Convergence ofNegative Order CesàroMeans of the Fourier–WalshSeries in L p (p > 1) Metrics”, J. Contemp.Math. Anal., Armen. Acad. Sci. 47, No. 3, 134–147 (2012).

    MathSciNet  MATH  Google Scholar 

  8. Zygmund, A. Trigonometric Series (Cambrige, 1959), Vol. 1.

    Google Scholar 

  9. Hardy, G. H. Divergent Series (Clarendon Press, Oxford, 1949; In. Lit., Moscow, 1951).

    Google Scholar 

  10. Golubov, B. I., Efimov, A. F., Skvortzov, V. A. Walsh’s Series and Transforms (Nauka, Moscow, 1987).

    Google Scholar 

  11. D’yachenko, M. I. “The Hardy–Littlewood Theorem for Trigonometric Series with Generalized Monotone Coefficients”, RussianMathematics (Iz. VUZ) 52, No. 5, 32–40 (2008).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yerevan State University, ul. Al. Manukyana 1, Yerevan, 0025, Republic of Armenia

    L. N. Galoyan

Authors
  1. L. N. Galoyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. N. Galoyan.

Additional information

Original Russian Text © L.N. Galoyan, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 2, pp. 24–30.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Galoyan, L.N. On L p-convergence of Cesàro means for Fourier series with monotonic coefficients. Russ Math. 60, 19–24 (2016). https://doi.org/10.3103/S1066369X16020043

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X16020043

Keywords

Search

Navigation