Resumen de The Bergman kernel and projection on non-smooth worm domains

Steven G. Krantz, Marco M. Peloso

• We study the Bergman kernel and projection on the worm domain of Diederich-Fornaess, as later modified by Christer Kiselman. We calculate the Bergman kernels explicitly for these domains, up to an error term that can be controlled. As a result, we can determine the Lp-mapping properties of the Bergman projections on these worm domains. We calculate the sharp range of p for which the Bergman projection is bounded on Lp. Along the way, we give a new proof of the failure of Condition R on these worms.

  Finally, we are able to show that the singularities of the Bergman kernel on the boundary are not contained in the boundary diagonal.