{"paper":{"title":"Some notes on commutators of the fractional maximal function on variable Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jianglong Wu, Pu Zhang, Zengyan Si","submitted_at":"2019-01-21T09:24:10Z","abstract_excerpt":"Let $0<\\alpha<n$ and $M_{\\alpha}$ be the fractional maximal function. The nonlinear commutator of $M_{\\alpha}$ and a locally integrable function $b$ is given by $[b,M_{\\alpha}](f)=bM_{\\alpha}(f)-M_{\\alpha}(bf)$. In this paper, we mainly give some necessary and sufficient conditions for the boundedness of $[b,M_{\\alpha}]$ on variable Lebesgue spaces when $b$ belongs to Lipschitz or $BMO(\\rn)$ spaces, by which some new characterizations for certain subclasses of Lipschitz and $BMO(\\rn)$ spaces are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06835","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"}