{"paper":{"title":"T1 theorem on product Carnot-Caratheodory spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chin-Cheng Lin, Ji Li, Yongsheng Han","submitted_at":"2012-09-27T14:09:30Z","abstract_excerpt":"Nagel and Stein established $L^p$-boundedness for a class of singular integrals of NIS type, that is, non-isotropic smoothing operators of order 0, on spaces $\\widetilde{M}=M_1\\times...\\times M_n,$ where each factor space $M_i, 1\\leq i\\leq n,$ is a smooth manifold on which the basic geometry is given by a control, or Carnot--Carath\\'eodory, metric induced by a collection of vector fields of finite type. In this paper we prove the product $T1$ theorem on $L^2,$ the Hardy space $H^p(\\widetilde{M})$ and the space $CMO^p(\\widetilde{M})$, the dual of $H^p(\\widetilde{M}),$ for a class of product sin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6236","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"}