{"paper":{"title":"Three observations on commutators of Singular Integral Operators with BMO functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos P\\'erez, Israel P. Rivera-R\\'ios","submitted_at":"2016-01-13T10:35:15Z","abstract_excerpt":"This paper contains three observations on commutators of Singular Integral Operators with BMO functions:\n  1) The subgaussian local decay for the commutator, namely \\[\\frac{1}{|Q|}\\left|\\left\\{x\\in Q\\, : \\, |[b,T](f\\chi_Q)(x)|>M^2f(x)t\\right\\}\\right|\\leq c e^{-\\sqrt{ct\\|b\\|_{BMO}}} \\] is sharp, that is, it is subgaussian and not better.\n  2) It is not possible to obtain a pointwise control of the commutator by a finite sum of sparse operators defined with $L\\log L$ averages.\n  3) If $w\\in A_p\\setminus A_1$ then $\\left\\| wM\\left(\\frac{f}{w}\\right)\\right\\|_{L^1(\\mathbb{R}^n)\\rightarrow L^{1,\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03193","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"}