Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with $C^2$ boundary
Year: 2026
Type: preprint
Abstract: On every bounded pseudoconvex domain $Ω\Subset\mathbb C^n$, $n\ge2$, with $C^2$ boundary, we prove $K_Ω/S_Ω\le C_{Ω,\varepsilon} δ_Ω^{-1}|\logδ_Ω|^{1+\varepsilon}$ near the boundary for every $\varepsilon>0$, where $δ_Ω$ denotes the boundary distance. For each positive nondecreasing $H(s)=o(s)$, a smoothly bounded pseudoconvex complete Reinhardt domain in $\mathbb C^2$ shows that the logarithmic factor cannot be replaced by $H(|\logδ_Ω|)$.
Source: arXiv (Cornell University)
Author: Xing, Xu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223378887