一维直线上的奇异型Trudinger-Moser不等式  

A FRACTIONAL SINGULAR TRUDINGER-MOSER INEQUALITY IN DIMENSION ONE

作　　者：朱茂春 刘杰[1] ZHU Mao-chun;LIU Jie(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013

出　　处：《数学杂志》2021年第3期219-226,共8页Journal of Mathematics

基　　金：国家自然科学基金(12071185,12061010,11971202);江苏省青年基金(BK20160483);江苏大学基础基金(16JDG043)资助.

摘　　要：本文研究了一维直线上的奇异型Trudinger-Moser不等式.利用分数次Sobolev空间上函数的Green表示公式,得到了一类奇异型Trudinger-Moser不等式.进一步利用合适的测试函数序列验证了不等式中常数的最佳性.这一结果将高维空间上的奇异型Trudinger-Moser不等式推广到了一维情形.This paper is devoted to studying a singular fractional Trudinger-Moser inequality in dimension one.By the Green representation formula for functions in the fractional Sobolev spaces,we get a singular fractional Trudinger-Moser type inequality.Furthermore,by using a suitable test functions sequence,we can show that the constant in the inequality is optimal.This result extends the singular Trudinger-Moser inequality in the high-dimensional spaces to the space of dimension one.

关 键 词：Trudinger-Moser不等式 分数次Sobolev空间 重排 最佳常数 

分 类 号：O178[理学—数学]