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

Valentina Casarino; Michael 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 Cowling, Alessio Martini, Adam Sikora

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

152 Downloads (Pure)

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 language	English
Pages (from-to)	3302-3338
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

Couchy-Riemann complex
Kohn Lapacian
multiplier theorem

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10.1007/s12220-017-9806-3Licence: None: All rights reserved

Casarino_et_al_Spectral_multipliers_for_the_Kohn_Laplacian_on_forms_on_the_sphere_in_Cn_Journal_of_Geometric_Analysis_2017
The final publication is available at Springer via http://dx.doi.org/10.1007/s12220-017-9806-3 Details verified: 13/3/2017
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Cite this

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

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

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T1 - Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn

AU - Casarino, Valentina

AU - Cowling, Michael

AU - Martini, Alessio

AU - Sikora, Adam

PY - 2017/10

Y1 - 2017/10

N2 - 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 .

AB - 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 .

KW - Couchy-Riemann complex

KW - Kohn Lapacian

KW - multiplier theorem

U2 - 10.1007/s12220-017-9806-3

DO - 10.1007/s12220-017-9806-3

M3 - Article

SN - 1050-6926

VL - 27

SP - 3302

EP - 3338

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 4

ER -