The Bergman kernel and projection on non-smooth worm domains

2007/06/25 by Steven G. Krantz, Krantz, Steven G., Marco M. Peloso +1
Mathematics · #32A25 #32A36 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.AP #math.CV #msc:32A25 #msc:32A36

paper · pdf · doi:10.48550/arxiv.0706.3708

arxiv created 2007/06/25 · openalex publication_date 2007/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the failure of Condition R, to deviant boundary behavior of the kernel, and to L^p mapping properties of the kernel.

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