Heisenberg型群上的一类带有余项的含权Hardy不等式

A class of weighted Hardy inequalities with remainderterms for Heisenberg type group

研究了Heisenberg型群上的一类带有余项的含权Hardy不等式的推广问题。利用散度定理并选择恰当的向量场,得到一类带有余项的含权Hardy不等式。结合逼近的方法,给出了最佳常数的证明,进一步推广了已有结果。

The problem of the improved versions to a class of weighted Hardy inequalities with remainder terms for Heisenberg type group is presented.By using divergence theorem and choosing suitable vector fields,a class of weighted Hardy inequalities with remainder terms is obtained.Furthermore,it is shown that the proof of the best constants by combining with the approximation method.Our results extend the existed results.