{"paper":{"title":"Integrating holomorphic $L^1$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A.-K. Herbig","submitted_at":"2013-03-21T10:33:51Z","abstract_excerpt":"Let $\\Omega\\Subset\\mathbb{C}^{n}$ be a domain with smooth boundary, $k\\in\\mathbb{N}$. It is shown that the integral of a holomorphic function in $L^1(\\Omega)$ may be represented as the integral of this function against a smooth function vanishing to order $k-1$ on $b\\Omega$. An application for a smoothing property of the Bergman projection for conjugate holomorphic functions is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5220","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"}