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Summability of Fourier series with the method
of lacunary arithmetical means
at the Lebesgue points

Author: E. S. Belinsky
Journal: Proc. Amer. Math. Soc. 125 (1997), 3689-3693
MSC (1991): Primary 42A16, 42A24
MathSciNet review: 1425111
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Abstract: The existence of the `rare' sequence of partial sums summable with the method of arithmetical means at each Lebesgue point is proved in the paper. The proof is based on the strategy of random choice.

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

  • [Al] Alexits, G., Convergence problems of orthogonal series, Pergamon Press, N.-Y.,Oxford, London, Paris, 1961. MR 36:1911
  • [Bl] Belinskii, E., On the summability of Fourier series with the method of lacunary arithmetical means, Analysis Math. 10 (4) (1984). MR 86i:42005
  • [Br1] Bourgain, J., Sur les sommes de sinus, Harmonic analysis: study group on translation-invariant Banach spaces, vol. N 3, Publ. Math. Orsay, 83, Univ. Paris XI, Orsay, 1983. MR 85d:44003
  • [Br2] Bourgain, J., Bounded orthogonal sets and the $\Lambda (p)$-problem, Acta Mathematica 162 (1989), 227-246. MR 90h:43008
  • [JLL] Long, Jui Lin, Sommes partielles de Fourier des fonctions bornees, Bull. Sci. Math. 105 (1981), 367-391. MR 83i:42004
  • [Zl] Zalcwasser, Z., Sur la sommability des series de Fourier, Studia Mathematica 6 (1936), 82-88.
  • [Sl] Salem, R., On strong summability of Fourier series, Amer. J. of Mathematics 77 (1955), 393-403. MR 16:816c
  • [TZ] Trigub, R. and Zagorodnii, N., On one Salem's question, Theory of functions and mappings, Naukova Dumka, Kiev, 1979, pp. 97-101 (Russian). MR 81g:42008
  • [Cl] Carleson, L., Appendix to the paper by J.-P. Kahane and Y. Katznelson Series de Fourier des fonctions bornees, Studies in pure mathematics, Birkhauser, Basel-Boston, Mass., 1983, pp. 395-413. MR 87c:42006
  • [Zg] Zygmund, A., Trigonometric series, 2nd ed., Cambridge Univ. Press, Cambridge, 1959. MR 21:6498

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Additional Information

E. S. Belinsky
Affiliation: Department of Mathematics, University of Zimbabwe, PO Box MP 167, Mount Pleasant, Harare, Zimbabwe

Keywords: Fourier series, Lebesgue points
Received by editor(s): July 30, 1996
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1997 American Mathematical Society

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