{"paper":{"title":"Division of holomorphic functions and growth conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Emmanuel Mazzilli, William Alexandre","submitted_at":"2012-07-06T09:31:07Z","abstract_excerpt":"Let D be a strictly convex domain of C^n, f_1 and f_2 be two holomorphic functions defined on a neighborhood of closure of D and set X_l={z, f_l(z)=0}, l=1,2. Suppose that X_l\\cap bD is transverse for l=1 and l=2, and that X_1\\cap X_2 is a complete intersection. We give necessary conditions when n>1 and sufficient conditions when n=2 under which a function g to be written as g=g_1f_1+g_2f_2 with g_1 and g_2 in L^q(D), q\\in [1,+\\infty), or g_1 and g_2 in BMO(D). In order to prove the sufficient condition, we explicitly write down the functions g_1 and g_2 using integral representation formulas "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1565","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"}