{"paper":{"title":"A note on weak factorization of Meyer-type Hardy space via Cauchy integral operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Cristina Pereyra, Ji Li, Yongsheng Han","submitted_at":"2019-02-03T03:57:52Z","abstract_excerpt":"This paper provides a weak factorization for the Meyer-type Hardy space $H^1_b(\\mathbb{R})$, and characterizations of its dual ${\\rm BMO}_b(\\mathbb{R})$ and its predual ${\\rm VMO}_b(\\mathbb{R})$ via boundedness and compactness of a suitable commutator with the Cauchy integral $\\mathscr{C}_{\\Gamma}$, respectively. Here $b(x)=1+iA'(x)$ where $A'\\in L^{\\infty}(\\mathbb{R})$, and the Cauchy integral $\\mathscr{C}_{\\Gamma}$ is associated to the Lipschitz curve $\\Gamma=\\{x+iA(x)\\, : \\, x\\in \\mathbb{R}\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00839","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"}