Vol. 16, No. 3, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
A theorem of Littlewood and lacunary series for compact groups

Alessandro Figà-Talamanca and Daniel Rider

Vol. 16 (1966), No. 3, 505–514
Abstract

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
Milestones
Received: 1 April 1965
Published: 1 March 1966
Authors
Alessandro Figà-Talamanca
Daniel Rider