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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 (33 #7774)
  • [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 (38 #6296)
  • [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 (38 #4882)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612724-X
PII: S 0002-9939(1981)0612724-X
Article copyright: © Copyright 1981 American Mathematical Society