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 Heisenbe...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.展开更多
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）
文摘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.
