{"paper":{"title":"Compactness of Riesz transform commutator associated with Bessel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dongyong Yang, Huoxiong Wu, Ji Li, Suzhen Mao, Xuan Thinh Duong","submitted_at":"2016-04-09T00:20:31Z","abstract_excerpt":"Let $\\lambda>0$ and $\\triangle_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x} \\frac d{dx}$ be the Bessel operator on $\\mathbb R_+:=(0,\\infty)$. We first introduce and obtain an equivalent characterization of ${\\rm CMO}(\\mathbb R_+,\\, x^{2\\lambda}dx)$. By this equivalent characterization and establishing a new version of the Fr\\'{e}chet-Kolmogorov theorem in the Bessel setting, we further prove that a function $b\\in {\\rm BMO}(\\mathbb R_+,\\, x^{2\\lambda}dx)$ is in ${\\rm CMO}(\\mathbb R_+,\\, x^{2\\lambda}dx)$ if and only if the Riesz transform commutator $[b, R_{\\Delta_\\lambda}]$ is compact on $L^p("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02503","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"}