International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 47, Pages 2517-2523
doi:10.1155/S016117120430921X
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 Laith Emil Azar. 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
We investigate the following problem: for a given A≥0, find
the infimum of the set of B≥0 such that the inequality
‖x(k)‖22≤A‖x(r)‖22+B‖x‖22, for k,r∈ℕ∪{0}, 0≤k<r, holds for all sufficiently
smooth functions.