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An extension of the Garrett-Stanojevic class

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Approximation Theory and its Applications

Abstract

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.

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References

  1. Sheng Shuyun, The Extension of the Theorems of C.V. Stanojecvic and V. B. Stanojevic, Proc. Amer. Math. Soc., 110 (1990), 895–904.

    Article  MATH  MathSciNet  Google Scholar 

  2. Tomovski, Z., A note on Some Classes of Fourier Coefficients, Math. Inequalities and Applications, 2 (1999), 15–18.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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. Stanojevic, C. V. and Stanojecvic, V. B., Generalizations of the Sidon-Teljakovskii Theorem, Proc. Amer. Math. Soc., 101 (1987), 679–684.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Tomovski Zivorad.

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Zivorad, T. An extension of the Garrett-Stanojevic class. Approx. Theory & its Appl. 16, 46–51 (2000). https://doi.org/10.1007/BF02845228

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  • DOI: https://doi.org/10.1007/BF02845228

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