The 𝐿_{𝑝} convergence of Fourier-Bessel series for 0<𝑝<1

Standish, Charles

doi:10.1090/S0002-9939-1957-0094637-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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The $L_{p}$ convergence of Fourier-Bessel series for $0<p<1$
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by Charles Standish

Proc. Amer. Math. Soc. 8 (1957), 484-486

DOI: https://doi.org/10.1090/S0002-9939-1957-0094637-4

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References

Lynn H. Loomis, A note on the Hilbert transform, Bull. Amer. Math. Soc. 52 (1946), 1082–1086. MR 19155, DOI 10.1090/S0002-9904-1946-08713-3
G. Milton Wing, The mean convergence of orthogonal series, Amer. J. Math. 72 (1950), 792–808. MR 37923, DOI 10.2307/2372296

Trigonometrical series

G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746