Restriction Theorems on Métiver Groups Associated to Joint Functional Calculus

Abstract

The authors get on Métivier groups the spectral resolution of a class of operators [inline-graphic not available: see fulltext], 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 $\mathcal{P}_\mu^m$ for two classes of functions m(a, b) = (a ^α + b ^β)^γ or (1 + a ^α + b ^β)^γ, with α, β > 0, γ ≠ 0.

Keywords

Restriction operator / Métivier group / Functional calculus

References

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