The growth of the bergman kernel on pseudoconvex domains of homogeneous finite diagonal type

DOI10.1017/S0027763000003986zbMath0782.32019MaRDI QIDQ4711247

Gregor Herbort

Publication date: 25 June 1992

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Bergman kernelplurisubharmonic weight functionspseudoconvex bumping\(L^ 2\)-theory for \(\bar\partial\)holomorphic squareintegrable functions

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Pseudoconvex domains (32T99)

Related Items

Positivity and completeness of invariant metrics ⋮ Boundary behavior of the Bergman kernel function on pseudoconvex domains with comparable Levi form. ⋮ Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in \(\mathbb{C}^2\) ⋮ An explicit computation of the Bergman kernel function

Cites Work

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• The Bergman kernel on uniformly extendable pseudoconvex domains
• Estimates of invariant metrics on pseudoconvex domains of dimension two
• Real hypersurfaces, orders of contact, and applications
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Logarithmic growth of the Bergman kernel for weakly pseudoconvex domains in \({\mathbb C}^ 3\) of finite type
• A pseudo-convex domain not admitting a holomorphic support function
• Über die 1. und 2. Ableitung der Bergmanschen Kernfunktion und ihr Randverhalten