THE FUNDAMENTAL SOLUTION TO □bON QUADRIC MANIFOLDS WITH NONZERO EIGENVALUES

Albert Boggess; Andrew Raich

doi:10.1090/btran/121

THE FUNDAMENTAL SOLUTION TO □_bON QUADRIC MANIFOLDS WITH NONZERO EIGENVALUES

Albert Boggess, Andrew Raich

Mathematical and Statistical Sciences, School of (SoMSS)

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

1 Scopus citations

Abstract

This paper is part of a continuing examination into the geometric and analytic properties of the Kohn Laplacian and its inverse on general quadric submanifolds of Cⁿ × C^m. The goal of this article is explore the complex Green operator in the case that the eigenvalues of the directional Levi forms are nonvanishing. We (1) investigate the geometric conditions on M which the eigenvalue condition forces, (2) establish optimal pointwise upper bounds on complex Green operator and its derivatives, (3) explore the L^p and L^p-Sobolev mapping properties of the associated kernels, and (4) provide examples.

Original language	English (US)
Pages (from-to)	507-541
Number of pages	35
Journal	Transactions of the American Mathematical Society Series B
Volume	10
DOIs	https://doi.org/10.1090/btran/121
State	Published - 2023

Keywords

L regularity
Quadric submanifolds
complex Green operator
higher codimension
hypoellipticity
nonzero eigenvalues

ASJC Scopus subject areas

Mathematics (miscellaneous)

Access to Document

10.1090/btran/121

Cite this

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abstract = "This paper is part of a continuing examination into the geometric and analytic properties of the Kohn Laplacian and its inverse on general quadric submanifolds of Cn × Cm. The goal of this article is explore the complex Green operator in the case that the eigenvalues of the directional Levi forms are nonvanishing. We (1) investigate the geometric conditions on M which the eigenvalue condition forces, (2) establish optimal pointwise upper bounds on complex Green operator and its derivatives, (3) explore the Lp and Lp-Sobolev mapping properties of the associated kernels, and (4) provide examples.",

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AB - This paper is part of a continuing examination into the geometric and analytic properties of the Kohn Laplacian and its inverse on general quadric submanifolds of Cn × Cm. The goal of this article is explore the complex Green operator in the case that the eigenvalues of the directional Levi forms are nonvanishing. We (1) investigate the geometric conditions on M which the eigenvalue condition forces, (2) establish optimal pointwise upper bounds on complex Green operator and its derivatives, (3) explore the Lp and Lp-Sobolev mapping properties of the associated kernels, and (4) provide examples.

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