On first order interpolation inequalities with weights on the H-type group

摘要

In this paper, sufficient and necessary conditions for a class of first order interpolation inequalities with weights on the H-type group are given. By polar coordinate changes of the H-type group, the necessity is verified. A class of Hardy type inequalities is established via a representation formula for functions, Hardy-Sobolev type inequalities are obtained by interpolation and then the sufficiency is completed through discussion of parameter sigma.