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| 摘要: |
| 本文研究Hardy型不等式及它的应用.首先从Heisenberg群上加权次椭圆p-Laplace不等方程出发,得到非负Lipschitz函数的Caccioppoli不等式,然后利用该不等式导出了关于另一Lipschitz函数的Hardy型不等式,进而推出一个精确Hardy-Poincaré不等式.需要强调的是,我们这里的Hardy型不等式是对于1<p<∞而言的,且对无界的区域也成立. |
| 关键词: Heisenberg群 p-Laplace不等方程 Hardy型不等式 Lipschitz函数 |
| DOI： |
| 分类号:O178 |
| 基金项目:国家自然科学基金(11771354) |
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| HARDY-TYPE INEQUALITY DERIVED FROM WEIGHTED SUB-ELLIPTIC $p$-LAPLACE INEQUALITY ON THE HEISENBERG GROUP AND ITS APPLICATION |
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ZHANG Jun-li
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| Abstract: |
| This paper studies Hardy-type inequality and its application. We firstly obtain the Caccioppoli inequality for nonnegative Lipschitz function from weighted sub-elliptic p-Laplace inequality. We use this inequality to derive Hardy-type inequality of another Lipschitz function, and then achieve an exact Hardy-Poincaré inequalitiy. It should be emphasized that the Hardy-type inequality here is for 1<p<∞ and also holds for unbounded regions. |
| Key words: Heisenberg group p-Laplace inequality hardy-type inequality Lipschitz function |
