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arXiv · 1501.02321

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

Valentina Casarino·Michael G. Cowling·Alessio Martini·Adam Sikora
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Abstract

The unit sphere $\mathbb{S}$ in $\mathbb{C}^n$ is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian $\Box_b$. We prove a Hörmander spectral multiplier theorem for $\Box_b$ 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 $\mathbb{S}$.

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Valentina Casarino, Michael G. Cowling, Alessio Martini, Adam Sikora. 2015-03-19. Spectral multipliers for the Kohn Laplacian on forms on the sphere in $\mathbb{C}^n$. https://doi.org/10.1007/s12220-017-9806-3

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