Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ESTIMATES OF THE BERGMAN KERNEL FUNCTION ON PSEUDOCONVEX DOMAINS WITH COMPARABLE LEVI FORM

  • Published : 2002.05.01
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Abstract

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^{n}$ and let $z^{0}$ $\in$b$\Omega$ a point of finite type. We also assume that the Levi form of b$\Omega$ is comparable in a neighborhood of $z^{0}$ . Then we get precise estimates of the Bergman kernel function, $K_{\Omega}$(z, w), and its derivatives in a neighborhood of $z^{0}$ . .

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References

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  1. Geometry of pseudo-convex domains of finite type with locally diagonalizable Levi form and Bergman kernel vol.85, pp.1, 2006, https://doi.org/10.1016/j.matpur.2005.10.001
  2. Boundary Integrals of the Bergman Kernel pp.1793-6519, 2018, https://doi.org/10.1142/S0129167X18710015
  3. Bergman–Toeplitz operators on weakly pseudoconvex domains pp.1432-1823, 2019, https://doi.org/10.1007/s00209-018-2096-z