Double trigonometric series with coefficients of bounded variation of higher order

Authors

  • Kulwinder Kaur
  • S. S. Bhatia
  • Babu Ram

DOI:

https://doi.org/10.5556/j.tkjm.35.2004.208

Abstract

In this paper the following convergence properties are established for the rectangular partial sums of the double trigonometric series, whose coefficients form a null sequence of bounded variation of order $ (p,0) $, $ (0,p) $ and $ (p,p) $, for some $ p\ge 1$: (a) pointwise convergence; (b) uniform convergence; (c) $ L^r $-integrability and $ L^r $-metric convergence for $ 0<{1\over p}$. Our results extend those of Chen [2, 4, 5] and M'oricz [7, 8, 9] and Stanojevic [10].

Author Biography

Kulwinder Kaur

Department of Mathematics, Maharshi Dyanand University, Rohtak, India.

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Published

2004-09-30

How to Cite

Kaur, K., Bhatia, S. S., & Ram, B. (2004). Double trigonometric series with coefficients of bounded variation of higher order. Tamkang Journal of Mathematics, 35(3), 267-280. https://doi.org/10.5556/j.tkjm.35.2004.208

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Papers