A Singular Moser-Trudinger Inequality on Metric Measure Space

查看全文 作　　者：GUI [1]Yaoting 机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China 出　　处：《Journal of Partial Differential Equations》索引2022年第35卷第4期,共13页 基　　金：supported by NSFC in China(No.11721101). 摘　　要：Let(X,d,μ)be a metric space with a Borel-measureμ,supposeμsatisfies the Ahlfors-regular condition,i.e.birs≤μu(Br(x))≤b2rs,VBr(x)CX,r>0,where bi,b2 are two positive constants and s is the volume growth exponent.In this paper,we mainly study two things,one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2.The other is to study the generalized Moser-Trudinger inequality with a singular Weight. 关 键 词：Metric measure space singular Moser-Trudinger inequality Ahlfors regularity