【摘 要】
：
The Hardy-Littlewood-Pólya (HLP) inequality [1] states that if a ∈ lp,b ∈ lq and p＞1,q＞1,1/p+1/q＞1,λ=2-(1/p+1/q),then ∑ r≠s (arbs)/(｜r-s｜λ )≤ C‖a‖p‖b‖q.
【机 构】
：
Department of Applied Mathematics
【基金项目】
：
Research supported by the NSF
论文部分内容阅读
The Hardy-Littlewood-Pólya (HLP) inequality [1] states that if a ∈ lp,b ∈ lq and p＞1,q＞1,1/p+1/q＞1,λ=2-(1/p+1/q),then ∑ r≠s (arbs)/(｜r-s｜λ )≤ C‖a‖p‖b‖q.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]:∑r≠s,1≤r,s≤N ( αrbs )/(｜r- s｜λ) ≤ (2lnN + 1)‖a‖2‖b‖2.In addition,we derive an accurate estimate for the best constant for this inequality.
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