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

Valentina Casarino, Michael G. Cowling*, Alessio Martini, Adam Sikora

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)3302-3338
    Number of pages37
    JournalJournal of Geometric Analysis
    Volume27
    Issue number4
    Early online date7 Mar 2017
    DOIs
    Publication statusPublished - Oct 2017

    Keywords

    • Cauchy–Riemann complex
    • Kohn Laplacian
    • Multiplier theorem

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