In this paper,we establish a sharp form of singular critical Hardy-Trudinger-Moser in-equality 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.
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