On the restricted Cesàro summability of double Fourier series
HTML articles powered by AMS MathViewer
- by A. J. White PDF
- Trans. Amer. Math. Soc. 99 (1961), 308-319 Request permission
References
- L. S. Bosanquet, A solution of the Cesàro summability problem for successively derived Fourier series, Proc. London Math. Soc. (2) 46 (1940), 270–289. MR 1978, DOI 10.1112/plms/s2-46.1.270 —, On the summability of Fourier series, Proc. London Math. Soc. (2) vol. 31 (1930) pp. 144-164.
- J. J. Gergen, Summability of double Fourier series, Duke Math. J. 3 (1937), no. 2, 133–148. MR 1545976, DOI 10.1215/S0012-7094-37-00310-7
- J. J. Gergen and S. B. Littauer, Continuity and summability for double Fourier series, Trans. Amer. Math. Soc. 38 (1935), no. 3, 401–435. MR 1501818, DOI 10.1090/S0002-9947-1935-1501818-9
- John G. Herriot, Nörlund summability of multiple Fourier series, Duke Math. J. 11 (1944), 735–754. MR 11142 E. W. Hobson, The theory of functions of a real variable. II, Cambridge, University Press, 1926.
- Charles N. Moore, On convergence factors in double series and the double Fourier’s series, Trans. Amer. Math. Soc. 14 (1913), no. 1, 73–104. MR 1500937, DOI 10.1090/S0002-9947-1913-1500937-6 R. E. A. C. Paley, On the Cesàro summability of Fourier series and allied series, Proc. Cambridge Philos. Soc. vol. 26 (1930) pp. 173-203. S. Saks, Remark on the differentiability of the Lebesgue indefinite integral, Fund. Math. vol. 22 (1934) pp. 257-261.
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 99 (1961), 308-319
- MSC: Primary 42.00; Secondary 40.00
- DOI: https://doi.org/10.1090/S0002-9947-1961-0121610-5
- MathSciNet review: 0121610