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An application of MVBV condition in real sense for L 1-convergence of trigonometric series

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Abstract

We continue to investigate the application of the Mean Value Bounded Variation (MVBV) concept in real sense, and prove the necessary and sufficient condition for L 1-convergence of trigonometric series.

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References

  1. L. Feng, V. Totik and S. P. Zhou, Trigonometric series with a generalized monotonicity condition, Acta Math. Sinica, English Ser., to appear.

  2. D. S. Yu, P. Zhou and S. P. Zhou, On L 1-convergence of Fourier series under MV BV condition, canad. math. bull., 52 (2009), 627–636.

  3. S. P. Zhou, Monotonicity Condition of Trigonometric Series: Development and Application, Science Press (Beijing, 2012), in Chinese.

  4. S. P. Zhou, P. Zhou and D. S. Yu, Ultimate generalization to monotonicity for uniform convergence of trigonometric series, Science China Math., 53 (2010), 1853– 1862/available: arXiv:math.CA/0611805 v1 27 Nov 2006.

  5. A. Zygmund, Trigonometric Series, Cambridge University Press (Cambridge, 1959).

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Correspondence to S. P. Zhou.

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Feng, L., Zhou, S.P. An application of MVBV condition in real sense for L 1-convergence of trigonometric series. Acta Math. Hungar. 144, 416–424 (2014). https://doi.org/10.1007/s10474-014-0438-9

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  • DOI: https://doi.org/10.1007/s10474-014-0438-9

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