An extension of discrete weighted Hardy-Littlewood-Sobolev inequality in space dimension one
An extension of discrete weighted Hardy-Littlewood-Sobolev inequality in space dimension one
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发表时间：
2015
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通讯作者：
Xu Jian
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作者：
Xu Jian
In this paper, we establish the critical version of discrete weighted Hardy-Littlewood-Sobolev inequality with p = q = 2, λ = 1 and α + β = 0 in R1:∑-N≤r,s≤N;r≠0,s≠0;r≠s(1/|r|α*arbs|s|α/|r-s|≤CαλαN‖a‖2‖b‖2) where a =(a-N,..., a N) and b =(b-N,..., b N). When α 1, we obtain that the sharp estimate λαNis Nα-1/2.Namely,∑-N≤r,s≤N;r≠0,s≠0;r≠s(1/|r|α*arbs|s|α/|r-s|≤CαNα-1/2‖a‖2‖b‖2)
