On integral representations for the Neumann operator

Abstract

This paper is devoted to the derivation of an approximate formula for the kernel of the Neumann operator N on strongly pseudo-convex domains. In particular, a new class of singular integral operators arises that are infinitely smoothing in the interior and preserve singular supports at the boundary and whose kernels are products of isotropic kernels with parabolic ones.

• complex Laplacian
• Hilbert integrals of mixed homogeneity
• subelliptic estimates