Restriction Theorems On Métiver Groups Associated to Joint Functional Calculus

In this article, we get the spectral solution $\mathcal{P}_μ^{m}$ of operators $m(\mathcal{L}, -Δ_\mathfrak{z})$, the joint functional calculus of the sub-Laplacian and Laplacian on the centre of Métivier group. Then, we give some group-analogues of the Thomas-Stein-type restriction theorem, asserting the mix-norm boundness of the restriction operators $\mathcal{P}_μ^{m}$ for two classes of functions $m=(a^α+b^β)^γ$ and $m=(1+a^α+b^β)^γ$ with $α, β>0, γ\neq0$.

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