{"paper":{"title":"Local regularity of the Green operator in a CR manifold of general \"type\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Giuseppe Zampieri, Luca Baracco, Stefano Pinton, Tran Vu Khanh","submitted_at":"2014-05-27T18:57:28Z","abstract_excerpt":"It is here proved that if a pseudoconvex CR manifold $M$ of hypersurface type has a certain \"type\", that we quantify by a vanishing rate $F$ at a submanifold of CR dimension $0$, then $\\Box_b$ \"gains $f^2$ derivatives\" where $f$ is defined by inversion of $F$. Indeed the estimate is more accurate and it involves the Levi form of $M$ and of additional weights, instead of $\\Box_b$. Next a general tangential estimate, \"twisted\" by a pseudodifferential operator $\\Psi$ is established. The combination of the two yields a general \"$f$-estimate\" twisted by $\\Psi$. We apply the twisted estimate for $\\P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7010","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"}