The Kohn-Laplacian and Cauchy-Szegö projection on model domains

Der-Chen Chang; Ji Li; Jingzhi Tie; Qingyan Wu

doi:10.4310/AMSA.2023.v8.n1.a4

The Kohn-Laplacian and Cauchy-Szegö projection on model domains

Der-Chen Chang, Ji Li, Jingzhi Tie, Qingyan Wu

School of Mathematical and Physical Sciences

Research output: Contribution to journal › Article

Abstract

We study the Kohn–Laplacian and its fundamental solution on some model domains in Cⁿ⁺¹, and further discuss the explicit kernel of the Cauchy–Szegö projections on these model domains using the real analysis method. We further show that these Cauchy–Szegö kernels are Calderón–Zygmund kernels under the suitable quasi-metric.

Original language	English
Pages (from-to)	111-155
Number of pages	45
Journal	Annals of Mathematical Sciences and Applications
Volume	8
Issue number	1
DOIs	https://doi.org/10.4310/AMSA.2023.v8.n1.a4
Publication status	Published - 2023

Keywords

CR manifolds
Cauchy-Szego~~projection
Heisenberg group
Kohn-Laplacian

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10.4310/AMSA.2023.v8.n1.a4

Cite this

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title = "The Kohn-Laplacian and Cauchy-Szeg{\"o} projection on model domains",

abstract = "We study the Kohn–Laplacian and its fundamental solution on some model domains in Cn+1, and further discuss the explicit kernel of the Cauchy–Szeg{\"o} projections on these model domains using the real analysis method. We further show that these Cauchy–Szeg{\"o} kernels are Calder{\'o}n–Zygmund kernels under the suitable quasi-metric.",

keywords = "CR manifolds, Cauchy-Szego~~projection, Heisenberg group, Kohn-Laplacian",

author = "Der-Chen Chang and Ji Li and Jingzhi Tie and Qingyan Wu",

year = "2023",

doi = "10.4310/AMSA.2023.v8.n1.a4",

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T1 - The Kohn-Laplacian and Cauchy-Szegö projection on model domains

AU - Chang, Der-Chen

AU - Li, Ji

AU - Tie, Jingzhi

AU - Wu, Qingyan

PY - 2023

Y1 - 2023

N2 - We study the Kohn–Laplacian and its fundamental solution on some model domains in Cn+1, and further discuss the explicit kernel of the Cauchy–Szegö projections on these model domains using the real analysis method. We further show that these Cauchy–Szegö kernels are Calderón–Zygmund kernels under the suitable quasi-metric.

AB - We study the Kohn–Laplacian and its fundamental solution on some model domains in Cn+1, and further discuss the explicit kernel of the Cauchy–Szegö projections on these model domains using the real analysis method. We further show that these Cauchy–Szegö kernels are Calderón–Zygmund kernels under the suitable quasi-metric.

KW - CR manifolds

KW - Cauchy-Szego~~projection

KW - Heisenberg group

KW - Kohn-Laplacian

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UR - http://purl.org/au-research/grants/arc/DP220100285

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DO - 10.4310/AMSA.2023.v8.n1.a4

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EP - 155

JO - Annals of Mathematical Sciences and Applications

JF - Annals of Mathematical Sciences and Applications

IS - 1

ER -

The Kohn-Laplacian and Cauchy-Szegö projection on model domains

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Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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The Kohn-Laplacian and Cauchy-Szegö projection on model domains

Abstract

Keywords

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Projects

DP22: Harmonic analysis of Laplacians in curved spaces

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