Heisenberg群中带奇异权的最优临界Hardy-Trudinger-Moser不等式

The sharp singular critical Hardy-Trudinger-Moser inequality of Heisenberg group

本文建立了Heisenberg群中有界域和一般无界域上带奇异权的最优临界Hardy-Trudinger-Moser不等式.克服临界Hardy不等式和奇异权函数带来的困难,利用带奇异权的Trudinger-Moser不等式和一些基本估计建立了有界域上一般的带奇异权的临界Hardy-Trudinger-Moser不等式,并通过选取适当的Moser函数得到了最佳常数.最后,利用分割积分区域的方法得到了一般无界域上带奇异权的最优临界Hardy-Trudinger-Moser不等式.

In this paper,we establish a sharp form of singular critical Hardy-Trudinger-Moser inequality in bounded and unbounded domain of Heisenberg group.We overcome the difficulties caused by critical Hardy inequalities and singular weighted functions,and then establish the singular critical Hardy-Trudinger-Moser inequality in bounded domain based on singular Trudinger-Moser inequality and some basic estimates.The best constants are obtained by choosing proper Moser functions.Finally,we prove sharp singular critical Hardy-Trudinger-Moser inequality by using the method of partitioning the integration domain.