Skip to main content
SpringerLink
Log in

Embedding results pertaining to strong approximation of Fourier series. VI

Теоремы вложения в терминах сильной аппроксимации рядом Фурье. VI

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

We verify a newer version of a certain embedding theorem pertaining to the relation being between strong approximation and a certain wide class of continuous functions. We also show that a new class of numerical sequences defined in this paper is not comparable to the class defined by Lee and Zhou, which is one of the largest among the classes being extensions of the class of monotone sequences.

Реэюме

Работа посвяшена усоверщенствованию одной теоремы вложения, которая выражает свяэь между сильной аппроксимацией и некоторым щироким классом непрерывных функций. Установлено также, что новый класс числовых последовательностей, понятие которого введено в данной работе, не сравним с классом, который был ранее введен в работе Ле и Жу, и был одним иэ самых щироких иэвестных обобшений класса монотонных последовательностей.

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. G. Alexits und D. Králik, Ü ber den Annäherungsgrad der Approximation in starken Sinne von stetigen funktionen, Magyar Tud. Akad. Mat. Kutató Int. Közl., 8(1963), 317–327.

    Google Scholar 

  2. G. Freud, Über die Sättigungsklasse der starken Approximation durch Teilsummen der Fourierschen Reihe, Acta Math. Acad. Sci. Hungar., 20(1969), 275–279.

    Article  MATH  MathSciNet  Google Scholar 

  3. V. G. Krotov and L. Leindler, On the strong summability of Fourier series and the classes H ω, Acta Sci. Math. (Szeged), 40(1978), 93–98.

    MATH  MathSciNet  Google Scholar 

  4. R.J. Lee and S.P. Zhou, A new condition for uniform convergence of certain trigonometric series, Acta Math. Hungar., 108(2005), 161–169.

    Article  MathSciNet  Google Scholar 

  5. L. Leindler, Embedding results pertaining to strong approximation of Fourier series. I, Analysis Math., 23(1997), 99–114.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Leindler, On the uniform convergence and boundedness of a certain class of sine series, Analysis Math., 27(2001), 279–285.

    Article  MATH  MathSciNet  Google Scholar 

  7. L. Leindler, Embedding results pertaining to strong approximation of Fourier series. IV, Analysis Math., 31(2005), 175–182.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Leindler, Embedding results regarding strong approximation of sine series, Acta Sci. Math. (Szeged), 71(2005), 91–103.

    MATH  MathSciNet  Google Scholar 

  9. L. Leindler, A new extension of monotone sequences and its applications, J. Inequal. Pure Appl. Math., 7(1)(2006), Article 39, http://jipam.vu.edu.au/article.php?sid=656.

Download references

Author information

Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary

    László Leindler

Authors
  1. László Leindler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to László Leindler.

Additional information

This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # T 042 462.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leindler, L. Embedding results pertaining to strong approximation of Fourier series. VI. Anal Math 34, 39–49 (2008). https://doi.org/10.1007/s10476-008-0104-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10476-008-0104-y

Keywords

Search

Navigation