| 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Hölder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. |
| 关键词: Dirac-调和方程 积分不等式 Radon测度 全局 |
| DOI： |
| 分类号:O175.5 |
| 基金项目:国家自然科学基金 (11461032); 江西省教育厅科技项目 (GJJ180446,GJJ170566). |
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| SOME INTEGRAL INEQUALITIES WITH RADON MEASURE |
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LI Hua-can1, LI Qun-fang2
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1.School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China;2.Department of Mathematics, Ganzhou Teachers College, Ganzhou 341000, China
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| Abstract: |
| In this paper, we study the problem of Radon integrability of differential forms satisfying the Dirac-harmonic equation. By two kind of Hölder inequalities, we flrst 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. |
| Key words: Dirac-harmonic equation integral inequalities Radon measure global |
