An extension of the hardy-littlewood-pólya inequality

The Hardy-Littlewood-Pólya (HLP) inequality [1] states that if a ∈ lp, b ∈ lqand then In this article, we prove the HLP inequality in the case where λ = 1, p = q = 2 with a logarithm correction, as conjectured by Ding [2]: In addition, we derive an accurate estimate for the best constant for this inequality.