Two-parameter estimates for joint spectral projections on complex spheres

Abstract

We prove sharp two-parameter estimates for the L p -L 2 norm, 1 ≤ p ≤ 2, of the joint spectral projectors associated to the Laplace–Beltrami operator and to the Kohn Laplacian on the unit sphere S 2n-1 in $${\mathbb{C}}^n$$ . Then, by using the notion of contraction of Lie groups, we deduce the estimates recently obtained by H. Koch and F. Ricci for joint spectral projections on the reduced Heisenberg group h 1.