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Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$ |
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| Authors: | Shutao Zhang & Yazhou Han |
| Abstract: | For conformal Hardy-Littlewood-Sobolev(HLS) inequalities 22] and reversed conformal HLS inequalities 8] on $\mathbb{S}^n,$ 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. |
| Keywords: | Hardy-Littlewood-Sobolev inequality reversed Hardy-Littlewood-Sobolev inequality rearrangement free method |
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