Restriction Theorems on Métiver Groups Associated to Joint Functional Calculus

The authors get on Métivier groups the spectral resolution of a class of operators , the joint functional calculus of the sub-Laplacian and Laplacian on the centre, and then give some restriction theorems together with their asymptotic estimates, asserting the mix-norm boundedness of the spectral projection operators $$\mathcal{P}_\mu^m$$Pμm for two classes of functions m(a, b) = (aα + bβ)γ or (1 + aα + bβ)γ, with α, β > 0, γ ≠ 0.