{"paper":{"title":"Bergman kernel and hyperconvexity index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen","submitted_at":"2016-10-22T08:49:55Z","abstract_excerpt":"Let $\\Omega\\subset {\\mathbb C}^n$ be a bounded domain with the hyperconvexity index $\\alpha(\\Omega)>0$. Let $\\varrho$ be the relative extremal function of a fixed closed ball in $\\Omega$ and set $\\mu:=|\\varrho|(1+|\\log|\\varrho||)^{-1}$, $\\nu:=|\\varrho|(1+|\\log|\\varrho||)^n$. We obtain the following estimates for the Bergman kernel: (1) For every $0<\\alpha<\\alpha(\\Omega)$ and $2\\le p<2+\\frac{2\\alpha(\\Omega)}{2n-\\alpha(\\Omega)}$, there exists a constant $C>0$ such that $\\int_\\Omega |\\frac{K_\\Omega(\\cdot,w)}{\\sqrt{K_\\Omega(w)}}|^{p}\\le C |\\mu(w)|^{-\\frac{(p-2) n}\\alpha}$ for all $w\\in \\Omega$. (2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07016","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}