Spectral multipliers for the Kohn Laplacian on forms on the sphere in ${\mathbb{C}}^n$

Abstract

The unit sphere $\mathbb{S}$ in ${\mathbb{C}}^n$ is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian ${\square }_b$. We prove a Hörmander spectral multiplier theorem for ${\square }_b$ with critical index $n-1/2$, that is, half the topological dimension of $\mathbb{S}$. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on $\mathbb{S}$.

arXiv comment28 pages

References in corpus (3)

• Spectral multiplier theorems of Euclidean type on new classes of 2-step stratified groups
• Hopf fibration: geodesics and distances
• L^p-summability of Riesz means for the sublaplacian on complex spheres

Cited by in corpus (5)

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• An $L^p$-spectral multiplier theorem with sharp $p$-specific regularity bound on Heisenberg type groups