Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains

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 $\bold C^n$. 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.

2010 Mathematics Subject Classification: Primary 32A36; Secondary 47B35, 47B06, 32W25

Keywords and Phrases: Dixmier trace, Toeplitz operator, Hankel operator, Bergman space, Hardy space, strictly pseudoconvex domain, pseudodifferential operator, Levi form

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