{"paper":{"title":"Duality of holomorphic functions spaces und smoothing properties of the Bergman projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anne-Katrin Herbig, Emil J. Straube, Jeffery D. McNeal","submitted_at":"2011-10-07T14:03:15Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{C}^n$ be a bounded domain with smooth boundary, whose Bergman projection $B$ maps the Sobolev space $H^{k_{1}}(\\Omega)$ (continuously) into $H^{k_{2}}(\\Omega)$. We establish two smoothing results: (i) the full Sobolev norm $\\|Bf\\|_{k_{2}}$ is controlled by $L^2$ derivatives of $f$ taken along a single, distinguished direction (of order $\\leq k_{1}$), and (ii) the projection of a conjugate holomorphic function in $L^{2}(\\Omega)$ is automatically in $H^{k_{2}}(\\Omega)$. There are obvious corollaries for when $B$ is globally regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1533","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"}