{"paper":{"title":"H\\\"ormander's solution of the $\\bar\\partial$ -equation with compact support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Amar (IMB)","submitted_at":"2016-04-16T13:07:56Z","abstract_excerpt":"This work is a complement of the study on H\\\"ormander's solution of the $\\bar\\partial$ equation initialised by H. Hedenmalm. Let $\\varphi$ be a strictly plurisubharmonic function of class C 2 in C n, let $c_\\varphi(z)$ be the smallest eigenvalue of $i\\partial\\bar\\partial\\varphi$ then $\\forall z\\in\\mathbb{C}^n$, $c_\\varphi (z)>0$. We denote by $L^2_{p,q}(\\mathbb{C}^n, e^\\varphi)$ the $(p, q)$ currents with coefficients in $L^2_{p,q}(\\mathbb{C}^n, e^\\varphi)$. We prove that if $\\omega\\in L^2_{p,q}(\\mathbb{C}^n,e^\\varphi)$, $\\bar\\partial$$\\omega$ = 0 for q <n then there is a solution u $\\in L ^2_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04744","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"}