The Diederich-Fornaess worm domain has proved to be of fundamental
importance in the understanding of the geometry of pseudoconvex domains in
multidimensional complex space. More recently, the worm has proved to be
an important example for the study of the inhomogeneous Cauchy-Riemann
equations in higher dimensions.
In forthcoming work, Krantz and Marco Peloso have done a complete
analysis of the Bergman kernel on a version of the worm domain.
We produce an asymptotic expansion for the kernel and calculate
its mapping properties. We can recover versions of the results
of Kiselman, Barrett, Christ, and Ligocka on the worm.