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In the present article, we provide a sufficient condition on a pair of nonnegative weight functions V and W on the Heisenberg group Hn, so that we establish a general Lp Hardy type inequality involving these weights with a remainder term. The method we use here is practical enough to get more weighted Hardy type inequalities. We also obtain new results on two-weight Hardy and Hardy-Poincaré type inequalities with remainder terms on Hn . Our findings improve and include many previously known results in special cases. Mathematics subject classification (2010): 26D10, 22E30, 43A80.

Weighted Hardy type inequalities on the Heisenberg group ℍ^n