Some theorems on 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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References | Similar Articles | 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**, https://doi.org/10.1090/S0002-9939-1956-0080796-5**[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****[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