TY - JOUR
T1 - Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$
AU - Zhang , Shutao
AU - Han , Yazhou
JO - Analysis in Theory and Applications
VL - 2
SP - 178
EP - 203
PY - 2022
DA - 2022/07
SN - 38
DO - http://doi.org/10.4208/ata.OA-2021-0025
UR - https://global-sci.org/intro/article_detail/ata/20798.html
KW - Hardy-Littlewood-Sobolev inequality, reversed Hardy-Littlewood-Sobolev inequality, rearrangement free method.
AB - <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>