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

Valentina Casarino; Michael G. Cowling; Alessio Martini; Adam Sikora

doi:10.1007/s12220-017-9806-3

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 journal › Article › peer-review

8 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 language	English
Pages (from-to)	3302-3338
Number of pages	37
Journal	Journal of Geometric Analysis
Volume	27
Issue number	4
Early online date	7 Mar 2017
DOIs	https://doi.org/10.1007/s12220-017-9806-3
Publication status	Published - Oct 2017

Keywords

Cauchy–Riemann complex
Kohn Laplacian
Multiplier theorem

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10.1007/s12220-017-9806-3

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title = "Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn",

abstract = "The unit sphere S in Cn is equipped with the tangential Cauchy–Riemann complex and the associated Laplacian □b. We prove a H{\"o}rmander 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.",

keywords = "Cauchy–Riemann complex, Kohn Laplacian, Multiplier theorem",

author = "Valentina Casarino and Cowling, {Michael G.} and Alessio Martini and Adam Sikora",

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AU - Casarino, Valentina

AU - Cowling, Michael G.

AU - Martini, Alessio

AU - Sikora, Adam

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

KW - Cauchy–Riemann complex

KW - Kohn Laplacian

KW - Multiplier theorem

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UR - http://purl.org/au-research/grants/arc/DP110102488

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DO - 10.1007/s12220-017-9806-3

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EP - 3338

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 4

ER -

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

Abstract

Keywords

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