For sub-Laplacians on Metivier groups, L^p spectral multiplier estimates hold at the sharp regularity threshold s > d|1/p - 1/2| for a range of p.
[M¨ ul89] , On Riesz means of eigenfunction expansions for the Kohn-Lap lacian, J
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Spectral multipliers on M\'etivier groups
For sub-Laplacians on Metivier groups, L^p spectral multiplier estimates hold at the sharp regularity threshold s > d|1/p - 1/2| for a range of p.