@Article{ATA-38-2,
author = {Zhang, Shutao and Yazhou, Han},
title = {Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$},
journal = {Analysis in Theory and Applications},
year = {2022},
volume = {38},
number = {2},
pages = {178--203},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2021-0025},
url = {https://global-sci.com/article/73756/rearrangement-free-method-for-hardy-littlewood-sobolev-inequalities-on-mathbbsn}
}