{"paper":{"title":"Exponential decay estimates for Singular Integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos P\\'erez, Carmen Ortiz-Caraballo, Ezequiel Rela","submitted_at":"2012-04-07T18:16:36Z","abstract_excerpt":"The following subexponential estimate for commutators is proved |[|\\{x\\in Q: |[b,T]f(x)|>tM^2f(x)\\}|\\leq c\\,e^{-\\sqrt{\\alpha\\, t\\|b\\|_{BMO}}}\\, |Q|, \\qquad t>0.\\] where $c$ and $\\alpha$ are absolute constants, $T$ is a Calder\\'on--Zygmund operator, $M$ is the Hardy Littlewood maximal function and $f$ is any function supported on the cube $Q$. It is also obtained \\[|\\{x\\in Q: |f(x)-m_f(Q)|>tM_{1/4;Q}^#(f)(x) \\}|\\le c\\, e^{-\\alpha\\,t}|Q|,\\qquad t>0,\\] where $m_f(Q)$ is the median value of $f$ on the cube $Q$ and $M_{1/4;Q}^#$ is Str\\\"omberg's local sharp maximal function. As a consequence it is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1666","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"}