| 各向异性Heisenberg群上一类强Hardy型不等式及其应用 |
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| 引用本文： | 王胜军,韩亚洲.各向异性Heisenberg群上一类强Hardy型不等式及其应用[J].四川师范大学学报(自然科学版),2011,34(1). |
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| 作者姓名： | 王胜军 韩亚洲 |
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| 作者单位： | 1. 青海师范大学数学与信息科学系,青海,西宁,810008
2. 中国计量学院数学系,浙江,杭州,310018 |
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| 基金项目： | 浙江省自然科学基金(Y606144)资助项目 |
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| 摘 要： | 通过推广、改进欧氏空间中的思想,对各向异性Heisenberg群上的Hardy型不等式给出了一个新证明.注意到原有许多结果中,由于使用方法的原因把原点排出在外,首先构造了一类C1向量场,结合逼近的思想不仅改进了这个缺陷而且得到常数cpQ,p的最佳性.作为应用,讨论了一类p次非线性算子的正定性与下无界性.
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| 关 键 词： | 各向异性Heisenberg群 正则化 强Hardy型不等式 |
Sharp Hardy Type Inequalities on Anisotropic Heisenberg Groups and Applications |
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| WANG Sheng-jun,HAN Ya-zhou.Sharp Hardy Type Inequalities on Anisotropic Heisenberg Groups and Applications[J].Journal of Sichuan Normal University(Natural Science),2011,34(1). |
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| Authors: | WANG Sheng-jun HAN Ya-zhou |
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| Institution: | WANG Sheng-jun1,HAN Ya-zhou2(1.Department of Mathematics and Information Sciences,Qinghai Normal University,Xining 810008,Qinghai,2.Department of Mathematics,China Jiliang University,Hangzhou 310018,Zhejiang) |
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| Abstract: | This paper presents a new proof of a class of Hardy type inequalities on anisotropic Heisenberg groups.Using regularization method by the careful choice of a suitable vector field in C1 and the approximating method,the obtained results not only contain the well-known results for sublaplace operator but also remedy a defect that eliminates the zero point in the existing results.Furthermore,the results get the best constant cpQ,p.As applications,the positive property and the unbounded property from below for ... |
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| Keywords: | anisotropic Heisenberg groups regularization sharp hardy type inequality |
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