On First Order Interpolation Inequalities with Weights on the Heisenberg Group  

On First Order Interpolation Inequalities with Weights on the Heisenberg Group

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作  者:Ya Zhou HAN Peng Cheng NIU Shu Tao ZHANG 

机构地区:[1]Department of Mathematics, College of Science, China diliang University, Hangzhou 310018, P. R. China [2]Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China [3]Department of Mathematics, College of Science, China Jiliang University, Hangzhou 310018, P. R. China

出  处:《Acta Mathematica Sinica,English Series》2011年第12期2493-2506,共14页数学学报(英文版)

基  金:Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6110118), National Natural Science Foundation of China (Grant No. 10871157) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200806990032)

摘  要:In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation, we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined.In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation, we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined.

关 键 词:Interpolation inequality Hardy-Sobolev type inequality Hardy type inequality Heisenberg group 

分 类 号:O175.3[理学—数学] O175.9[理学—基础数学]

 

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