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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 37, Pages 2345-2347
http://dx.doi.org/10.1155/S0161171203203045

The conjugation operator on Aq(G)

Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khaud 123, Oman

Received 5 March 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let q>2. We prove that the conjugation operator H does not extend to a bounded operator on the space of integrable functions defined on any compact abelian group with the Fourier transform in lq.