Weighted High Order Poincaré Inequalities on Stratified Lie Groups  

分层李群上的加权高阶Poincaré不等式

作　　者：HAN Yecong HUANG Tiren XU Chengdan ZHU Tingjing 韩烨琮;黄体仁;徐成丹;朱婷(华南理工大学数学学院,广东广州510630;浙江理工大学数学系,浙江杭州310018)

机构地区：[1]School of Mathematics,South China University of Technology,Guangzhou,Guangdong,510630,P.R.China [2]Department of Mathematics,Zhejiang Sci-Tech University,Hangzhou,Zhejiang,310018,P.R.China

出　　处：《数学进展》2024年第5期1071-1083,共13页Advances in Mathematics（China）

摘　　要：In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several Poincare inequalities that complement existing results,which have only been proved for the case 1<p<q<∞.本文主要研究分层李群上的加权Poincaré不等式.我们在高阶Sobolev空间W^(m,p)中得到了1<p=q<∞情形下的多种Poincaré不等式.这些不等式是对现有仅在1<p<q<∞的情况成立的Poincaré不等式的补充.

关 键 词：A_(p)weight Poincaréinequality entire space stratified Lie group high order Sobolev space 

分 类 号：O178[理学—数学]