{"paper":{"title":"The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Tuomas P. Hyt\\\"onen","submitted_at":"2018-04-30T12:59:39Z","abstract_excerpt":"Supplying the missing necessary conditions, we complete the characterisation of the $L^p\\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\\infty$ and under minimal non-degeneracy hypotheses on $T$.\n  For $p\\leq q$ (and especially $p=q$), this extends a long line of results under more restrictive assumptions on $T$. In particular, we answer a recent question of Lerner, Ombrosi, and Rivera-R\\'ios by showing that $b\\in BMO$ is necessary for the $L^p$-boundedness of $[b,T]$ for any non-zero homogeneous singular i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11167","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1804.11167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}