Notes on Fourier Analysis (XI) : On the absolute summability of Fourier series

Gen-ichirô SUNOUCHI

doi:10.2969/jmsj/00120122

Gen-ichirô SUNOUCHI

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JOURNAL FREE ACCESS

1949 Volume 1 Issue 2 Pages 122-129

DOI https://doi.org/10.2969/jmsj/00120122

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Published: 1949 Received: December 10, 1947 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Notes on Fourier Analysis (XI): On the absolute summability of Fourier series
Right : Notes on Fourier Analysis (XI) : On the absolute summability of Fourier series

Date of correction: August 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Gen-ichiro SUNOUCHI¹⁾
Right : Gen-ichirô SUNOUCHI¹⁾

Date of correction: August 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Mathematical Institute Tohoku University

Right :
1) Mathematical Institute Tôhoku University

Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) Bosanquet, L. S., and Kestleman, H., The absolute convergence of series of integrals, Proc. London Math. Soc., 48 (1938), 88-97.
2) Chen, K. K., Amer. Journ. of Math., 60 (1944).
3) Chow, H. C., On the absolute summability of Fourier series, Journ. London Math. Soc., 17 (1942), 17-22.
4) Izumi, S. and Kawata, T., Notes on Fourier series (III): Absolute summability, Proc. Imp. Acad. Tokyo, 14 (1938), 32-35.
5) Izumi, S. and Kawata, T., Notes on Fourier series (VIII): A remark on absolutely summable factors, Tohoku Math. Journ., 45 (1938), 194-196.
6) Kogbetlianz, E., Sur les séries absolument sommables par la methode des moyennes arithmétiques, Bull. Sci. Math., 60 (1925), 234-256.
7) Marcinkiewicz, J., Sur la sommabilité forte de series de Fourier, Journ. London Math. Soc., 14 (1949), 162-168.
8) Prasad, B. N., on the summability of Fourier series and the bounded variation of power series, Proc. London Math. Soc., 35 (1933), 407-424.
9) Tsuchikura, T., Notes on Fourier Analysis (III): Convergence character of Fourier series, in the press.
10) Zygmund, A., On the convergence and summability of power series on the circle of convergence (I), Fund. Math., 30 (1938), 170-196.
11) Zygmund, A., On certain integral, Trans. Amer. Math. Soc., 55 (1944).

Right : [1] Bosanquet, L. S., and Kestleman, H., The absolute convergence of series of integrals, Proc. London Math. Soc., 48 (1938), 88-97.
[2] Chen, K. K., Amer. Journ. of Math., 60 (1944).
[3] Chow, H. C., On the absolute summability of Fourier series, Journ. London Math. Soc., 17 (1942), 17-22.
[4] Izumi, S. and Kawata, T., Notes on Fourier series (III): Absolute summability, Proc. Imp. Acad. Tokyo, 14 (1938), 32-35.
[5] Izumi, S. and Kawata, T., Notes on Fourier series (VIII): A remark on absolutely summable factors, Tohoku Math. Journ., 45 (1938), 194-196.
[6] Kogbetlianz, E., Sur les séries absolument sommables par la méthode des moyennes arithmétiques, Bull. Sci. Math., 60 (1925), 234-256.
[7] Marcinkiewicz, J., Sur la sommabilité forte de series de Fourier, Journ. London Math. Soc., 14 (1949), 162-168.
[8] Prasad, B. N., On the summability of Fourier series and the bounded variation of power series, Proc. London Math. Soc., 35 (1933), 407-424.
[9] Tsuchikura, T., Notes on Fourier Analysis (III): Convergence character of Fourier series, in the press.
[10] Zygmund, A., On the convergence and summability of power series on the circle of convergence (I), Fund. Math., 30 (1938), 170-196.
[11] Zygmund, A., On certain integral, Trans. Amer. Math. Soc., 55 (1944).

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