| Heisenberg型群上一类精确Hardy型不等式和Hardy-Sobolev型不等式及应用(英文) |
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| 引用本文： | 王胜军,窦井波.Heisenberg型群上一类精确Hardy型不等式和Hardy-Sobolev型不等式及应用(英文)[J].数学进展,2012(2):177-186. |
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| 作者姓名： | 王胜军 窦井波 |
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| 作者单位： | 青海师范大学数学与信息科学系;西安财经学院统计学院 |
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| 基金项目： | supported by NSFC(No.10802061);Foundation of Shaanxi Province Education Department(No.2010JK549);the Foundation of Xi’an Statistical Research Institute(No.10JD04) |
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| 摘 要： | 本文在Heisenberg型群上建立了一类精确的Hardy型不等式。采用的技巧是逼近及正则化的方法。进一步利用这个结果,本文建立了一类精确的Hardy-Sobolev型不等式。这两个结果包括了已有的相关结果。作为应用,讨论了一类具有Hardy位势的非线性算子的正定性与下无界性。
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| 关 键 词： | Heisenberg型群 正则化 Hardy型不等式 Hardy-Sobolev型不等式 |
Sharp Hardy Type Inequalities and Hardy-Sobolev Type Inequalities on Heisenberg Type Group and Applications |
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| WANG Shengjun,DOU Jingbo.Sharp Hardy Type Inequalities and Hardy-Sobolev Type Inequalities on Heisenberg Type Group and Applications[J].Advances in Mathematics,2012(2):177-186. |
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| Authors: | WANG Shengjun DOU Jingbo |
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| Institution: | (2,**) (1.Department of Mathematics and Information Sciences,Qinghai Normal University,Xining, Qinghai,810008,P.R.China;2.School of Statistics,Xi’an University of Finance and Economics, Xi’an,Shaanxi,710100,P.R.China) |
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| Abstract: | In this paper,using regularization and approximating method,we prove a Hardy type inequality which contains the origin and improves the range of the index p on Heisenberg type group.Furthermore,we use this result to estabhsh a Hardy-Sobolev type inequality.Our results contain the existed relevant results.As applications,we discuss the positive property and the unbounded property from below for a nonlinear operator relating with the Hardy potential. |
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| Keywords: | Heisenberg type group regularization Hardy type inequality Hardy-Sobolev type inequality |
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