On two theorems of Paley

Rivière, N. M.; Sagher, Y.

doi:10.1090/S0002-9939-1974-0344779-0

On two theorems of Paley
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by N. M. Rivière and Y. Sagher PDF

Proc. Amer. Math. Soc. 42 (1974), 238-242 Request permission

Abstract:

A strengthening of Paley’s theorem for the Fourier coefficients of an ${L^p}$ function is presented. The result is then applied to prove strong versions of recent results of P. L. Duren, and of J. H. Hedlund on $({L^p},{L^q})$ multipliers.

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