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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 strong summability of Fourier series


Author: Gen-Ichirô Sunouchi
Journal: Proc. Amer. Math. Soc. 1 (1950), 526-533
MSC: Primary 42.4X
MathSciNet review: 0037385
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  • [1] R. P. Boas, Jr., and S. Bochner, On à theorem of M. Riesz for Fourier series, J. London Math. Soc. vol. 14 (1939) pp. 62-73.
  • [2] A. Kolmogoroff, Une contribution à l'étude de la convergence des séries de Fourier, Fund. Math. vol. 5 (1924) pp. 96-97.
  • [3] J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series, J. London Math. Soc. vol. 6 (1931) pp. 230-233.
  • [4] -, Theorems on Fourier series and power series, (2), Proc. London Math. Soc. (2) vol. 42 (1937) pp. 52-89.
  • [5] J. Marcinkiewicz and A. Zygmund, A theorem of Lusin. Part I, Duke Math. J. 4 (1938), no. 3, 473–485. MR 1546069, http://dx.doi.org/10.1215/S0012-7094-38-00440-5
  • [6] Gen-ichirô Sunouchi, On the strong summability of Fourier series, Proc. Imp. Acad. Tokyo 19 (1943), 420–423. MR 0014157 (7,247c)
  • [7] Z. Zalcwasser, Sur la sommabilité des séries de Fourier, Studia Mathematica vol. 6 (1936) pp. 82-88.
  • [8] A. Zygmund, Sur la caractère de divergence des séries orthogonales, Mathematica vol. 9 (1935) pp. 86-88.
  • [9] -, Proof of a theorem of Paley, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 125-133.
  • [10] -, On the convergence and summability of power series on the circle of convergence (1), Fund. Math. vol. 30 (1938) pp. 170-196.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1950-0037385-2
PII: S 0002-9939(1950)0037385-2
Article copyright: © Copyright 1950 American Mathematical Society