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Some theorems on $ L\sp{p}$ Fourier series


Author: Richard P. Gosselin
Journal: Trans. Amer. Math. Soc. 92 (1959), 291-301
MSC: Primary 42.00
DOI: https://doi.org/10.1090/S0002-9947-1959-0111975-3
MathSciNet review: 0111975
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  • [1] R. P. Gosselin, On the convergence of Fourier series of functions in an $ {L^p}$ class, Proc. Amer. Math. Soc. vol. 7, no. 3 (1956) pp. 392-397. MR 0080796 (18:303d)
  • [2] G. H. Hardy and J. E. Littlewood, Notes on the theory of series (XXIII): On the partial sums of Fourier series, Proc. Cambridge Philos. Soc. vol. 40 (1944) pp. 103-107. MR 0010629 (6:47f)
  • [3] S. Kacmarz and H. Steinhaus, Theorie der orthogonalreihen, New York, 1951.
  • [4] J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series, II and III, Proc. London Math. Soc. vol. 42 (1937) pp. 52-89; vol. 43 (1937) pp. 105-126.
  • [5] R. E. A. C. Paley, A remarkable series of orthogonal functions, Proc. London Math. Soc. vol. 34 (1932) pp. 241-279.
  • [6] A. Zygmund, Proof of a theorem of Paley, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 125-133.
  • [7] -, On the convergence and summability of power series on the circle of convergence, Fund. Math. vol. 30 (1938) pp. 170-196.
  • [8] -, Trigonometrical series, Warsaw, 1935.

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DOI: https://doi.org/10.1090/S0002-9947-1959-0111975-3
Article copyright: © Copyright 1959 American Mathematical Society

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