Year: 2022
Author: Shutao Zhang, Yazhou Han
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 178–203
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2021-0025
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 2 : pp. 178–203
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Hardy-Littlewood-Sobolev inequality reversed Hardy-Littlewood-Sobolev inequality rearrangement free method.