{"paper":{"title":"On CR Paneitz operators and CR pluriharmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.AP","authors_text":"Chin-Yu Hsiao","submitted_at":"2014-05-01T13:38:46Z","abstract_excerpt":"Let $(X,T^{1,0}X)$ be a compact orientable embeddable three dimensional strongly pseudoconvex CR manifold and let ${\\rm P\\,}$ be the associated CR Paneitz operator. In this paper, we show that (I) ${\\rm P\\,}$ is self-adjoint and ${\\rm P\\,}$ has $L^2$ closed range. Let $N$ and $\\Pi$ be the associated partial inverse and the orthogonal projection onto ${\\rm Ker\\,}{\\rm P\\,}$ respectively, then $N$ and $\\Pi$ enjoy some regularity properties. (II) Let $\\hat{\\mathcal{P}}$ and $\\hat{\\mathcal{P}_0}$ be the space of $L^2$ CR pluriharmonic functions and the space of real part of $L^2$ global CR function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0158","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"}