Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn

Valentina Casarino, Michael Cowling, Alessio Martini, Adam Sikora

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3 Citations (Scopus)
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Abstract


The unit sphere SS in CnCn is equipped with the tangential Cauchy–Riemann complex and the associated Laplacian □b◻b . We prove a Hörmander spectral multiplier theorem for □b◻b with critical index n−1/2n−1/2 , that is, half the topological dimension of SS . Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on SS .
Original languageEnglish
Pages (from-to)3302-3338
JournalJournal of Geometric Analysis
Volume27
Issue number4
Early online date7 Mar 2017
DOIs
Publication statusPublished - Oct 2017

Keywords

  • Couchy-Riemann complex
  • Kohn Lapacian
  • multiplier theorem

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