Geodesic
Hankel operators and the Dixmier trace on strictly pseudoconvex domains
Documenta mathematica, Tome 15 (2010), pp. 601-622
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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 Cn. 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.
DOI : 10.4171/dm/308
Classification : 32A36, 32W25, 47B06, 47B35
Mots-clés : Bergman space, pseudodifferential operator, Dixmier trace, Toeplitz operator, Hankel operator, Hardy space, strictly pseudoconvex domain, Levi form 
@article{10_4171_dm_308,
     author = {Miroslav Englis},
     title = {Hankel operators and the {Dixmier} trace on strictly pseudoconvex domains},
     journal = {Documenta mathematica},
     pages = {601--622},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/308},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/308/}
}
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Miroslav Englis. Hankel operators and the Dixmier trace on strictly pseudoconvex domains. Documenta mathematica, Tome 15 (2010), pp. 601-622. doi: 10.4171/dm/308

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