Authors:S. Jitendriya, R. Radha, and D. Venku Naidu
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 Rj
and 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.