The fundamental solution to □ _b on quadric manifolds: part 2. L^p regularity and invariant normal forms

This paper is the second of a multi-part series in which we explore geometric and analytic properties of the Kohn–Laplacian and its inverse on general quadric submanifolds of Cⁿ× C^m. We have two goals in this paper. The first is to give useable sufficient conditions for a map T between quadrics to be a Lie group isomorphism that preserves □ _b, and the second is to establish a framework for which appropriate derivatives of the complex Green operator are continuous in L^p and L^p-Sobolev spaces (and hence are hypoelliptic). We apply the general results to codimension two quadrics in C⁴.