Skip to main content
SpringerLink
Log in

Remarks on some classes of Fourier coefficients

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

In this paper equivalent classes of the classes M' α and S' p α r, p >1, α≥0,r ∈{0,1,2,...,[α]} defined by Sheng [5] are obtained. Then it is shown that the classes of Fourier coefficients S p, S' p(case r=α=0) and S p(δ), p>1, defined by Č. V. Stanojević, V. B. Stanojević Sheng and the author of the present note are identical. As a corollary of this result, the L 1-estimate for cosine series, obtained in [10], is refined.

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. R. P. Boas, Quasi-positive sequence and trigonometric series, Proc. London. Math. Soc., 14(1965), 38–46.

    Google Scholar 

  2. H. Bor, Integrability of Rees-Stanojević sums, Tamkang J. Math., 15(1984), 157–160.

    Google Scholar 

  3. L. Leindler, On the equivalence of classes of numerical sequences, Analysis Math., 26(2000), 227–234.

    Google Scholar 

  4. S. M. Mazhar, On generalized quasi-convex sequence and its application, Indian J. Pure Appl. Math., 8(1977), 784–790.

    Google Scholar 

  5. S. Sheng, The extensions of the theorems of Č. V. Stanojević and V. B. Stanojević, Proc. Amer. Math. Soc., 110(1990), 895–904.

    Google Scholar 

  6. N. Singh and K. M. Sharma, Convergence of certain sums in a metric space L 1, Proc. Amer. Math. Soc., 72(1978), 117–120.

    Google Scholar 

  7. Č. V. StanojeviĆ, AND V. B. StanojeviĆ, Generalization of the Sidon-Telyakovskii theorem, Proc. Amer. Math. Soc., 101(1987), 679–684.

    Google Scholar 

  8. S. A. Telyakovskii, On a sufficient condition of Sidon for the integrability of trigonometric series, Math. Zametki, 14(1973), 742–748 (in Russian).

    Google Scholar 

  9. С. А. ТЕЛЯКОВСКИЙ, Замечание об условиях интегрирыемости тригонометрических рядов, Весmнuк Моск. Ун-ma, серия 1, мат-мех., 4(2000), 58–60.

  10. Ž. Tomovski, An application of the Hausdorff-Young inequality, Math. Inequal. Appl., 1(1998), 527–532.

    Google Scholar 

  11. Ž. Tomovski, Necessary and sufficient condition for L1-convergence of cosine trigonometric series with δ-quasi-monotone coefficient, Math. Comm., 4(1999), 219–224.

    Google Scholar 

  12. Ž. Tomovski, New generalizations of the Telyakovskii inequalities, RGMIA Res. Rep. Coll., 5(2002), http://rgmia.vu.edu.au/v5n1.html.

  13. S. A. Zahid, Integrability of trigonometric series, Tamkang J. Math., 21(1990), 295–301.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematical and Natural Sciences, P.O.Box 162, 1000, Skopje, Macedonia

    Živorad Tomovski

Authors
  1. Živorad Tomovski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tomovski, Ž. Remarks on some classes of Fourier coefficients. Analysis Mathematica 29, 165–170 (2003). https://doi.org/10.1023/A:1023956511182

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023956511182

Keywords

Search

Navigation