Approximation Theory and its Applications

, Volume 16, Issue 1, pp 46–51 | Cite as

An extension of the Garrett-Stanojevic class



The extension is made for the theorem of [2], by considering the classes Spr and Cr, 1<p≤2, r∈{0,1,2,…} instead of Sp and C. Namely, it is shown that the class Spr is a subclass of Cr∩BV, 1<p≤2,r∈{0,1, 2,…}, where BV is the class of null sequences of bounded variation, and Cr, r∈{0,1,2…} is the extension of the Garrett-Stanojevci class.


Analytical Function Positive Constant Fourier Series Natural Science Periodic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Sheng Shuyun, The Extension of the Theorems of C.V. Stanojecvic and V. B. Stanojevic, Proc. Amer. Math. Soc., 110 (1990), 895–904.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Tomovski, Z., A note on Some Classes of Fourier Coefficients, Math. Inequalities and Applications, 2 (1999), 15–18.MATHMathSciNetGoogle Scholar
  3. [3]
    Garrett, J. W. and Stanojecvic, C. V., Necessary and Sufficient Condition forL 1-Convergence of Trigonometric Series, Proc. Amer. Math. Soc., 60 (1976), 68–71.CrossRefMathSciNetGoogle Scholar
  4. [4]
    Teliakovskii, S. A., On a Sufficient Condition of Sidon for the Integrability of Trigonometric Series, Math. Notes, 14 (1973), 742–748.Google Scholar
  5. [5]
    Stanojevic, C. V. and Stanojecvic, V. B., Generalizations of the Sidon-Teljakovskii Theorem, Proc. Amer. Math. Soc., 101 (1987), 679–684.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Garrett, J. W., Ress, C. S. and Stanojevic, C. V.,L 1-Convergence of Fourier Series with Coefficients of Bounded Variation, Proc. Amer. Math. Soc., 80 (1980), 423–430.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 2000

Authors and Affiliations

  1. 1.University of SkopjeMacedonia
  2. 2.Faculty of Mathematical and Natural SciencesSkopje Macedonia

Personalised recommendations