{"paper":{"title":"Equivalence of estimates on domain and its boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tran Vu Khanh","submitted_at":"2017-04-14T05:05:38Z","abstract_excerpt":"Let $\\Omega$ be a pseudoconvex domain in $\\mathbb C^n$ with smooth boundary $b\\Omega$. We define general estimates $(f\\text{-}\\mathcal M)^k_{\\Omega}$ and $(f\\text{-}\\mathcal M)^k_{b\\Omega}$ on $k$-forms for the complex Laplacian $\\Box$ on $\\Omega$ and the Kohn-Laplacian $\\Box_b$ on $b\\Omega$. For $1\\le k\\le n-2$, we show that $(f\\text{-}\\mathcal M)^k_{b\\Omega}$ holds if and only if $(f\\text{-}\\mathcal M)^k_{\\Omega}$ and $(f\\text{-}\\mathcal M)^{n-k-1}_{\\Omega}$ hold. Our proof relies on Kohn's method in [Ann. of Math. (2), 156(1):213--248, 2002]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04349","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"}