{"paper":{"title":"A note on $L^2$ boundary integrals of the Bergman kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Phung Trong Thuc","submitted_at":"2018-03-26T03:06:18Z","abstract_excerpt":"For any bounded convex domain $\\Omega$ with $C^{2}$ boundary in $\\mathbb{C}^{n}$, we show that there exist positive constants $C_{1}$ and $C_{2}$ such that \\[ C_{1}\\sqrt{\\dfrac{K\\left(w,w\\right)}{\\delta\\left(w\\right)}}\\leq\\left\\Vert K\\left(\\cdot,w\\right)\\right\\Vert _{L^{2}\\left(\\partial\\Omega\\right)}\\leq C_{2}\\sqrt{\\dfrac{K\\left(w,w\\right)}{\\delta\\left(w\\right)}}, \\] for any $w\\in\\Omega$. Here $K$ is the Bergman kernel of $\\Omega$, and $\\delta$ is the distance-to-boundary function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09393","kind":"arxiv","version":1},"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"}