In this paper, it is shown that the class of right Fourier multipliers for the Sobolev space Wk,p(Hn) coincides with the class of right Fourier multipliers for Lp(Hn) for k ∈ ℕ, 1 < p < ∞. Towards this end, it is shown that the operators RjR̄jℒ-1 and RjR̄jRjℒ-1 are bounded on Lp(Hn), 1 < p < ∞, ℒ is the sublaplacian on Hn. This proof is based on the Calderon-Zygmund theory on the Heisenberg group. It is also shown that when p = 1, the class of right multipliers for the Sobolev space Wk,1(Hn) coincides with the dual space of the projective tensor product of two function spaces. © 2010 Akadémiai Kiadó, Budapest, Hungary.