{"paper":{"title":"Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Dongyong Yang, Jin Tao","submitted_at":"2018-01-04T09:18:04Z","abstract_excerpt":"Let $C_\\Gamma$ be the Cauchy integral operator on a Lipschitz curve $\\Gamma$. In this article, the authors show that the commutator $[b,C_\\Gamma]$ is bounded (resp., compact) on the Morrey space $L^{p,\\,\\lambda}(\\mathbb R)$ for any (or some) $p\\in(1, \\infty)$ and $\\lambda\\in(0, 1)$ if and only if $b\\in {\\rm BMO}(\\mathbb R)$ (resp., ${\\rm CMO}(\\mathbb R)$). As an application, a factorization of the classical Hardy space $H^1(\\mathbb R)$ in terms of $C_\\Gamma$ and its adjoint operator is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04997","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"}