{"paper":{"title":"A Revisit on Commutators of linear and bilinear Fractional Integral Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mingming Cao, Qingying Xue","submitted_at":"2016-04-24T06:57:04Z","abstract_excerpt":"Let $I_{\\alpha}$ be the linear and $\\mathcal{I}_{\\alpha}$ be the bilinear fractional integral operators. In the linear setting, it is known that the two-weight inequality holds for the first order commutators of $I_{\\alpha}$. But the method can't be used to obtain the two weighted norm inequality for the higher order commutators of $I_{\\alpha}$. In this paper, we first give an alternative proof for the first order commutators of $I_{\\alpha}$. This new approach allows us to consider the higher order commutators. This was done by showing that the commutator $[b,I_{\\alpha}]$ can be represented as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06992","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"}