On Weighted Integrability of Double Cosine Series

  title={On Weighted Integrability of Double Cosine Series},
  author={Babu Ram and Satvinder Singh Bhatia},
  journal={Journal of Mathematical Analysis and Applications},
  • B. Ram, S. S. Bhatia
  • Published 15 April 1997
  • Mathematics
  • Journal of Mathematical Analysis and Applications
Abstract In this paper we study weighted integrability of the sum of double cosine series. The results obtained extend a theorem of 5 onLp-integrability of double cosine series and two theorems of 1 on weightedLp-norms. 
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We extend from one-dimensional to two-dimensional series the results by Hardy and Littlewood [6] on the Lr-integrability of the sum f and the results by Stechkin [10] on the L'-integrability of the
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(x) is not in general Lebesgue integrable in (0, n) [2, p. 7881. He also proved that for 0 < y < 1 a function like xP’ near 0 has a cosine series whose coefficients behave at infinity like n7-l and
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  • J. London Ž . Math. Soc
  • 1931