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 Cn × Cm. 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 C4 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