## Abstract

This paper is the first of a three part series in which we explore geometric and analytic properties of the Kohn Laplacian and its inverse on general quadric submanifolds of C^{n} × C^{m}. In this paper, we present a streamlined calculation for a general integral formula for the complex Green operator N and the projection onto the nullspace of □_{b} . The main application of our formulas is the critical case of codimension two quadrics in C^{4} wherewediscuss the known solvability and hypoellipticity criteria of Peloso and Ricci [J. Funct. Anal. 203 (2003), pp. 321–355] We also provide examples to show that our formulas yield explicit calculations in some well-known cases: the Heisenberg group and a Cartesian product of Heisenberg groups.

Original language | English (US) |
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Pages (from-to) | 186-203 |

Number of pages | 18 |

Journal | Proceedings of the American Mathematical Society, Series B |

Volume | 9 |

DOIs | |

State | Published - 2022 |

## Keywords

- Complex Green operator
- Heisenberg group
- Quadric submanifolds
- Szegö kernel
- Szegö projection
- Tangential Cauchy-Riemann operator
- fundamental solution
- ∂

## ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Discrete Mathematics and Combinatorics
- Geometry and Topology

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