Fourier multipliers for Sobolec spaces on the Heisenberg group (Q555501)

It is proved that the class of right Fourier multipliers for the Sobolev space \(W^{k,p}(H^n)\) coincides with the class of right Fourier multipliers for the Lebesgue space \(L^p(H^n)\), where \(H^n\) is the \(n\)-dimensional Heisenberg group, \(k\in \mathbb{N}\) and \(p\in ]0,\infty[\). The proof of this result is based on the Calderón-Zygmund theory of the Heisenberg group. It is also shown that the class of right multipliers for \(W^{k,1}(H^n)\) agrees with the dual space of the projective tensor product of two function spaces.