Comparison of the Bergman and Szegö kernels

Bo Yong Chen, Siqi Fu

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

The quotient of the Szegö and Bergman kernels for a smooth bounded pseudoconvex domains in Cn is bounded from above by a constant multiple of δ|logδ|p for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of D'Angelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ|logδ|p for any p<-1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.

Original languageEnglish (US)
Pages (from-to)2366-2384
Number of pages19
JournalAdvances in Mathematics
Volume228
Issue number4
DOIs
StatePublished - Nov 10 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 32A25
  • 32U35
  • 32W05
  • Bergman kernel
  • Diederich-Fornæss exponent
  • L2-estimate
  • Pluricomplex Green function
  • Szegö kernel
  • ∂-operator

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