{"paper":{"title":"Spectral multipliers for the Kohn Laplacian on forms on the sphere in $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Adam Sikora, Alessio Martini, Michael G. Cowling, Valentina Casarino","submitted_at":"2015-01-10T08:53:39Z","abstract_excerpt":"The unit sphere $\\mathbb{S}$ in $\\mathbb{C}^n$ is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian $\\Box_b$. We prove a H\\\"ormander spectral multiplier theorem for $\\Box_b$ with critical index $n-1/2$, that is, half the topological dimension of $\\mathbb{S}$. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on $\\mathbb{S}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02321","kind":"arxiv","version":2},"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"}