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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 45-48, Pages 2517-2523
doi:10.1155/S016117120430921X

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

Laith Emil Azar

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

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.