A geometric characterization: complex ellipsoids and the Bochner-Martinelli kernel

Abstract

Boas' characterization of bounded domains for which the Bochner-Martinelli kernel is self-adjoint is extended to the case of a weighted measure. For strictly convex domains, this equivalently characterizes the ones whose Leray-Aĭzenberg kernel is self-adjoint with respect to weighted measure. In each case, the domains are complex linear images of a ball, and the measure is the Fefferman measure. The Leray-Aĭzenberg kernel for a strictly convex hypersurface in $\mathbb{C}^n$ is shown to be Möbius invariant when defined with respect to Fefferman measure.