Some theorems on Fourier series
Author:
Richard P. Gosselin
Journal:
Trans. Amer. Math. Soc. 92 (1959), 291301
MSC:
Primary 42.00
MathSciNet review:
0111975
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References 
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Additional Information
 [1]
Richard
P. Gosselin, On the convergence of Fourier series
of functions in an 𝐿^{𝑝} class, Proc. Amer. Math. Soc. 7 (1956), 392–397. MR 0080796
(18,303d), http://dx.doi.org/10.1090/S00029939195600807965
 [2]
G.
H. Hardy and J.
E. Littlewood, Note on the theory of series. XXIII. On the partial
sums of Fourier series, Proc. Cambridge Philos. Soc.
40 (1944), 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. 5289; vol. 43 (1937) pp. 105126.
 [5]
R. E. A. C. Paley, A remarkable series of orthogonal functions, Proc. London Math. Soc. vol. 34 (1932) pp. 241279.
 [6]
A. Zygmund, Proof of a theorem of Paley, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 125133.
 [7]
, On the convergence and summability of power series on the circle of convergence, Fund. Math. vol. 30 (1938) pp. 170196.
 [8]
, Trigonometrical series, Warsaw, 1935.
 [1]
 R. P. Gosselin, On the convergence of Fourier series of functions in an class, Proc. Amer. Math. Soc. vol. 7, no. 3 (1956) pp. 392397. 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. 103107. 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. 5289; vol. 43 (1937) pp. 105126.
 [5]
 R. E. A. C. Paley, A remarkable series of orthogonal functions, Proc. London Math. Soc. vol. 34 (1932) pp. 241279.
 [6]
 A. Zygmund, Proof of a theorem of Paley, Proc. Cambridge Philos. Soc. vol. 34 (1938) pp. 125133.
 [7]
 , On the convergence and summability of power series on the circle of convergence, Fund. Math. vol. 30 (1938) pp. 170196.
 [8]
 , Trigonometrical series, Warsaw, 1935.
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DOI:
http://dx.doi.org/10.1090/S00029947195901119753
PII:
S 00029947(1959)01119753
Article copyright:
© Copyright 1959 American Mathematical Society
