{"paper":{"title":"Boundedness and compactness of commutators associated with Lipschitz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dongyong Yang, Huoxiong Wu, JIanxun He, Weichao Guo","submitted_at":"2018-01-17T05:09:42Z","abstract_excerpt":"Let $\\alpha\\in (0, 1]$, $\\beta\\in [0, n)$ and $T_{\\Omega,\\beta}$ be a singular or fractional integral operator with homogeneous kernel $\\Omega$. In this article, a CMO type space ${\\rm CMO}_\\alpha(\\mathbb R^n)$ is introduced and studied. In particular, the relationship between ${\\rm CMO}_\\alpha(\\mathbb R^n)$ and the Lipchitz space $Lip_\\alpha(\\mathbb R^n)$ is discussed. Moreover, a necessary condition of restricted boundedness of the iterated commutator $(T_{\\Omega,\\beta})^m_b$ on weighted Lebesgue spaces via functions in $Lip_\\alpha(\\mathbb R^n)$, and an equivalent characterization of the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06064","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"}