摘要
For conformal Hardy-Littlewood-Sobolev(HLS)inequalities[22]and reversed conformal HLS inequalities[8]on S^(n),a new proof is given for the attainability of their sharp constants.Classical methods used in[22]and[8]depends on rearrangement inequalities.Here,we use the subcritical approach to construct the extremal sequence and circumvent the blow-up phenomenon by renormalization method.The merit of the method is that it does not rely on rearrangement inequalities.
基金
supported by the National Natural Science Foundation of China(Grant No.12071269)
Natural Science Foundation of Zhejiang Province(Grant No.LY18A010013).
