关于Radon测度的积分不等式  

SOME INTEGRAL INEQUALITIES WITH RADON MEASURE

作　　者：李华灿[1] 李群芳 LI Hua-can;LI Qun-fang(School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China;Department of Mathematics,Ganzhou Teachers College,Ganzhou 341000,China)

机构地区：[1]江西理工大学理学院,江西赣州341000 [2]赣州师范高等专科学校数学系,江西赣州341000

出　　处：《数学杂志》2019年第6期899-906,共8页Journal of Mathematics

基　　金：国家自然科学基金(11461032);江西省教育厅科技项目(GJJ180446,GJJ170566)

摘　　要：本文研究了满足Dirac-调和方程的微分形式Radon积分问题.利用两种形式的Holder不等式,首先得到了作用于满足Dirac-调和方程的微分形式上的关于Radon测度的局部Poincaré-型不等式,然后以此为基础,综合运用积分技巧与Whitney覆盖等相关性质进一步得到δ-John域上全局的Poincaré-型不等式.上述结果推广了微分形式的积分理论.In this paper, we study the problem of Radon integrability of differential forms satisfying the Dirac-harmonic equation. By two kind of H?lder inequalities, we first obtain the local Poincaré-type inequality applying to differential forms which satisfy Dirac-harmonic equation.Then, based on the local result, we also obtain the global Poincaré-type inequality on δ-John domain by use of some proper integral skills and the property of Whitney cover, which generalized the integral theory differential form.

关 键 词：Dirac-调和方程 积分不等式 RADON测度 全局 

分 类 号：O175.5[理学—数学]