On First Order Interpolation Inequalities with Weights on the Heisenberg Group

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

作者机构：Department of Mathematics College of Science China diliang University Hangzhou 310018 P. R. China Department of Applied Mathematics Northwestern Polytechnical University Xi＇an 710072 P. R. China Department of Mathematics College of Science China Jiliang University Hangzhou 310018 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第12期

页      面：2493-2506页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：Interpolation inequality Hardy-Sobolev type inequality Hardy type inequality Heisenberg group 

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.