Function Spaces and Their Operators
A Conference in Honor of Richard Rochberg on the Occasion of his 65th Birthday

Miroslav Englis from Silesian University, Czech Republic; Toeplitz operators, weighted Bergman kernels, and Dixmier traces; May 29, 2008.

Abstract: The celebrated theorem of Fefferman describes the boundary singularity of the Bergman kernel of a strictly pseudoconvex domain in $\bold C^n$. We give a generalization of this result to certain weighted Bergman spaces, in whose proof, perhaps surprisingly, Toeplitz operators turn out to play the crucial role. Time permitting, we~briefly outline also another application of the same technique, involving the Dixmier traces of Hankel operators. The last is a joint work with Guo-Zhang and Rochberg.