Kodai Mathematical Journal

On the summability almost everywhere of the multiple Fourier series at the critical index

Gen-ichirô Sunouchi

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 8, Number 1 (1985), 1-4.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138036991

Digital Object Identifier
doi:10.2996/kmj/1138036991

Mathematical Reviews number (MathSciNet)
MR0776701

Zentralblatt MATH identifier
0575.42017

Subjects
Primary: 42B05: Fourier series and coefficients
Secondary: 42A24: Summability and absolute summability of Fourier and trigonometric series

Citation

Sunouchi, Gen-ichirô. On the summability almost everywhere of the multiple Fourier series at the critical index. Kodai Math. J. 8 (1985), no. 1, 1--4. doi:10.2996/kmj/1138036991. https://projecteuclid.org/euclid.kmj/1138036991


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References

  • [1] CALDERON, C. P., Lacunary spherical means, Illinois Journ. Math., 23 (1979), 476-484.
  • [2] SAGHER, Y., On analytic families of operators, Israel Journ. Math., 7 (1969), 350-356.
  • [3] SJOLIN, P., An inequality of Paley and convergence a.e. of Walsh Fourier series, Arkiv for Mat., 7 (1968), 551-570.
  • [4] STEIN, E. M., Localization and summability of multiple Fourier series, Acta Math., 100 (1958), 93-147.
  • [5] STEIN, E. M., An H1 function with non-summable Fourier expansion, Lecture notes in Math., No.992, Springer, 1983, Harmonic analysis, Proc. Conf. Cortona, Italy, 193-200.
  • [6] SUNOUCHI, G., A Fourier series which belongs to the class H divergesalmost everywhere, Kodai Math. Seminar Rep., 5 (1953), 27-28.
  • [7] ZYGMUND, A., Trigonometric series, Cambridge Univ. Press, 1959.