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On the absolute logarithmic summability of a Fourier series and its differentiated series


Authors: R. Mohanty and S. Mahapatra
Journal: Proc. Amer. Math. Soc. 7 (1956), 254-259
MSC: Primary 40.0X
MathSciNet review: 0077677
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References [Enhancements On Off] (What's this?)

  • [1] L. S. Bosanquet, Note on the absolute summability (C) of a Fourier series, J. London Math. Soc. vol. 11 (1936) pp. 11-16.
  • [2] -, The absolute Cesàro summability of a Fourier series, Proof of Theorem 1 with $ \beta > 1$. Proc. London Math. Soc. vol. 41 (1936) pp. 517-528.
  • [3] R. Mohanty, On the absolute Riesz summability of Fourier series and allied series, Proc. London Math. Soc. (2) 52 (1951), 295–320. MR 0041266
  • [4] -, On the summability $ \vert R,\log,1\vert$ of a Fourier series, J. London Math. Soc. vol. 25 (1950) pp. 57-72.
  • [5] E. C. Titchmarsh, Theory of functions, Oxford, 1939, p. 409.
  • [6] A. Zygmund, Trigonometrical series, 1935, p. 35.

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DOI: https://doi.org/10.1090/S0002-9939-1956-0077677-X
Article copyright: © Copyright 1956 American Mathematical Society