{"paper":{"title":"The $\\bar{\\partial}$-Neumann operator with the Sobolev norm of integer orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Bingyuan Liu, Phillip Harrington","submitted_at":"2019-05-10T16:12:47Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{C}^m$ be a bounded pseudoconvex domain with smooth boundary. For each $k\\in\\mathbb{N}$, we give a sufficient condition to estimate the $\\bar\\partial$-Neumann operator in the Sobolev space $W^k(\\Omega)$. The key feature of our results is a precise formula for $k$ in terms of the geometry of the boundary of $\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04238","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"}