The unit sphere S in C^n is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian. We prove a Hoermander spectral multiplier theorem for this Laplacian with critical index n-1/2, that is, half the topological dimension of S. Our proof is mainly based on some tools of representation theory and on a fine analysis of the spaces of differential forms on S.
Spectral multipliers for the Kohn Laplacian on forms on the sphere in C^n
CASARINO, VALENTINA;
2017
Abstract
The unit sphere S in C^n is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian. We prove a Hoermander spectral multiplier theorem for this Laplacian with critical index n-1/2, that is, half the topological dimension of S. Our proof is mainly based on some tools of representation theory and on a fine analysis of the spaces of differential forms on S.File in questo prodotto:
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