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For the maps on the Heisenberg group target, we prove a Poincaré type inequality.Applying this Poincaré type inequality, we obtain the corresponding versions of Sobolev and Rellich embedding theorems. §1 IntroductionThe Heisenberg group H n (see [3]) is the Lie group whose underlying manifold is C n × R with n ∈ N, endowed with the group law algebra g = R 2n+1 and a nonablian group law (z, t) · (z , t ) = (z + z , t + t + 2 Im (z · z )), ∀z, z ∈ C n , t,t ∈ R,(1.