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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 47, Pages 2517-2523

Some exact inequalities of Hardy-Littlewood-Polya type for periodic functions

Department of Mathematics, Al Al-Bayt University, Mafraq 25113, Jordan

Received 28 September 2003

Copyright © 2004 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.


We investigate the following problem: for a given A0, find the infimum of the set of B0 such that the inequality x(k)22Ax(r)22+Bx22, for k,r{0}, 0k<r, holds for all sufficiently smooth functions.