Vol. 16, No. 3, 1966

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A theorem of Littlewood and lacunary series for compact groups

Alessandro Figà-Talamanca and Daniel Rider

Vol. 16 (1966), No. 3, 505–514

Let G be a compact group and f L2(G). We prove that given p < there exists a unitary transformation U of L2(G) into L2(G), which commutes with left translations and such that Uf Lp. The proof is based on techniques developed by S. Helgason for a similar question. The result stated above, which is an extension of a theorem of Littlewood for the unit circle is then applied to the study of lacunary Fourier series.

Mathematical Subject Classification
Primary: 42.50
Received: 1 April 1965
Published: 1 March 1966
Alessandro Figà-Talamanca
Daniel Rider