Hankel operators and the Dixmier trace on strictly pseudoconvex domains

Abstract

Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of $2n$ Hankel operators on Bergman spaces of strictly pseudoconvex domains in ${\mathbf{C}}^n$. The answer turns out to involve the dual Levi form evaluated on boundary derivatives of the symbols. Our main tool is the theory of generalized Toeplitz operators due to Boutet de Monvel and Guillemin.