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arXiv · 2610.31043

Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with $C^2$ boundary

Xu Xing
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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 $H(|\logδ_Ω|)$.

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Xu Xing. 2026-10-22. Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with $C^2$ boundary. https://arxiv.org/abs/2610.31043

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