Analysis in Theory and Applications

, Volume 27, Issue 1, pp 32–39 | Cite as

Integrability and L 1-convergence of double cosine trigonometric series

Article

Abstract

We study here L 1-convergence of new modified double cosine trigonometric sum and obtain a new necessary and sufficient condition for L 1-convergence of double cosine trigonometric series. Also, the results obtained by Moricz[1],[2] are particular cases of ours.

Key words

L1-convergence conjugate Dirichlet kernel 

AMS (2010) subject classification

42A20 42A32 

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References

  1. [1]
    Móricz, F., Integrability of Double Trigonometric Series with Special Coefficients, Anal. Math., 16 (1990), 39–56.CrossRefMATHMathSciNetGoogle Scholar
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    Móricz, F., On the Integrability and L 1-convergence of Double Trigonometric Series, StudiaMath., 98:3(1991), 203–225.MATHGoogle Scholar
  3. [3]
    Kaur, J. and Bhatia, S.S., Convergence of New Modified Trigonometric Sums in The Metric Space L, The Journal of Nonlinear Sciences and Applications, 1:3(2008), 179–188.MATHMathSciNetGoogle Scholar
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    Sheng, S., The Extension of the Theorems of Č.V.Stanojević and V.B.Stanojević, Proc. Amer. Math. Soc., 110 (1990), 895–904.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Editorial Board of Analysis in Theory and Applications and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematics & Computer ApplicationsThapar UniversityPatialaIndia

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