Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality
Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality
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DOI：
10.3934/dcds.2015.35.935
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发表时间：
2013-09
期刊：
影响因子：
--
通讯作者：
Genggeng Huang;Congming Li;Ximing Yin
中科院分区：
文献类型：
--
作者：
Genggeng Huang;Congming Li;Ximing Yin
In this paper, we study the best constant of the following discrete Hardy-Littlewood-Sobolev inequality, \begin{equation} \sum_{i,j,i\neq j}\frac{f_{i}g_{j}}{\mid i-j\mid^{n-\alpha}}\leq C_{r,s,\alpha} |f|_{l^r} |g|_{l^s}, \end{equation}where $i,j\in \mathbb Z^n$, $r,s>1$, $0 2$.
In this paper, we study the best constant of the following discrete Hardy-Littlewood-Sobolev inequality, \begin{equation} \sum_{i,j,i\neq j}\frac{f_{i}g_{j}}{\mid i-j\mid^{n-\alpha}}\leq C_{r,s,\alpha} |f|_{l^r} |g|_{l^s}, \end{equation}where $i,j\in \mathbb Z^n$, $r,s>1$, $0 2$.