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Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with C2 boundary
Abstract
On every bounded pseudoconvex domain ΩSubsetℂn, n≥2, with C2 boundary, we prove KΩ/SΩ≤ CΩ,ε δΩ−1|logδΩ|1+ε near the boundary for every ε>0, where δΩ denotes the boundary distance. For each positive nondecreasing H(s)=o(s), a smoothly bounded pseudoconvex complete Reinhardt domain in ℂ2 shows that the logarithmic factor cannot be replaced by H(|logδΩ|).
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BibTeX
@misc{xing2026comparison,
title = {{Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with $C^2$ boundary}},
author = {Xu Xing},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31043},
eprint = {2610.31043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31043},
}
RIS
TY - UNPB
TI - Comparison of the Bergman and Szegő kernels on arbitrary bounded pseudoconvex domains with C^2 boundary
AU - Xu Xing
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31043
UR - https://arxiv.org/abs/2610.31043
AB - On every bounded pseudoconvex domain ΩSubsetℂ^n, n≥2, with C^2 boundary, we prove K_Ω/S_Ω≤ C_Ω,ε δ_Ω^−1|logδ_Ω|^1+ε near the boundary for every ε>0, where δ_Ω denotes the boundary distance. For each positive nondecreasing H(s)=o(s), a smoothly bounded pseudoconvex complete Reinhardt domain in ℂ^2 shows that the logarithmic factor cannot be replaced by H(|logδ_Ω|).
ER -