{"paper":{"title":"A refinement of the Berezin-Li-Yau type inequality for nonlocal elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Yong-Cheol Kim","submitted_at":"2014-06-19T11:35:27Z","abstract_excerpt":"In this paper, we prove a refinement of the Berezin-Li-Yau type inequality for a wider class of nonlocal elliptic operators including the fractional Laplacians $-(-\\Delta^{\\sm/2})$ restricted to a bounded domain $D\\subset\\BR^n$ for $n\\ge 2$ and $\\sm\\in (0,2]$, which is optimal when $\\sigma=2$ in view of Weyl's asymptotic formula. In addition, we describe the Berezin-Li-Yau inequality for the Laplacian $\\Delta$ as the limit case of our result as $\\sm\\to 2^-$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5407","kind":"arxiv","version":2},"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"}