{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IQRNJQW75TU6ANCIKCQ3UHXBFB","short_pith_number":"pith:IQRNJQW7","schema_version":"1.0","canonical_sha256":"4422d4c2dfece9e0344850a1ba1ee12847ed1c7d8255764d68d04a02ed92e04c","source":{"kind":"arxiv","id":"1604.04744","version":1},"attestation_state":"computed","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$$\\omega$ = 0 for q 0$. We denote by $L^2_{p,q}(\\mathbb{C}^n, e^\\varphi)$ the $(p, q)$ currents with coefficients in $L^2_{p,q}(\\mathbb{C}^n, e^\\varphi)$. We prove that if $\\omega\\in L^2_{p,q}(\\mathbb{C}^n,e^\\varphi)$, $\\bar\\partial$$\\omega$ = 0 for q