The Bergman kernel and projection on non-smooth worm domains

• Autores: Steven G. Krantz, Marco M. Peloso
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 3, 2008, págs. 873-950
• Idioma: inglés
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• Resumen

  • 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.