Archivio Istituzionale della RicercaThe unit sphere S in Cn is equipped with the tangential Cauchy–Riemann complex and the associated Laplacian □ b. We prove a Hörmander spectral multiplier theorem for □ b with critical index n- 1 / 2 , that is, half the topological dimension of S. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on S.
Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn / Casarino, V.; Cowling, M. G.; Martini, A.; Sikora, A.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 27:4(2017), pp. 3302-3338. [10.1007/s12220-017-9806-3]
Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn
Casarino V.;Martini A.;
2017
Abstract
The unit sphere S in Cn is equipped with the tangential Cauchy–Riemann complex and the associated Laplacian □ b. We prove a Hörmander spectral multiplier theorem for □ b with critical index n- 1 / 2 , that is, half the topological dimension of S. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on S.
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Casarino2017_Article_SpectralMultipliersForTheKohnL.pdf
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complexspheres-revised.pdf
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https://hdl.handle.net/11583/2949480