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On the Dini test and divergence of Fourier series

Author: Calixto P. Calderón
Journal: Proc. Amer. Math. Soc. 82 (1981), 382-384
MSC: Primary 42A20
MathSciNet review: 612724
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Abstract: In this note we prove that no condition weaker than the Dini assures the pointwise convergence of a Fourier series in a set of positive measure.

References [Enhancements On Off] (What's this?)

  • [1] Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157. MR 0199631,
  • [2] Richard A. Hunt, On the convergence of Fourier series, Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967) Southern Illinois Univ. Press, Carbondale, Ill., 1968, pp. 235–255. MR 0238019
  • [3] J. Marcinkiewicz, Sur les séries de Fourier, Fund. Math. 27 (1936), 38-69.
  • [4] -, On the convergence of Fourier Series, J. London Math. Soc. 10 (1935), 264-268.
  • [5] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968. MR 0236587

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