{"paper":{"title":"Improved Cotlar's inequality in the context of local $Tb$ theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Henri Martikainen, Mihalis Mourgoglou, Xavier Tolsa","submitted_at":"2015-12-09T17:18:55Z","abstract_excerpt":"We prove in the context of local $Tb$ theorems with $L^p$ type testing conditions an improved version of Cotlar's inequality. This is related to the problem of removing the so called buffer assumption of Hyt\\\"onen-Nazarov, which is the final barrier for the full solution of S. Hofmann's problem. We also investigate the problem of extending the Hyt\\\"onen-Nazarov result to non-homogeneous measures. We work not just with the Lebesgue measure but with measures $\\mu$ in $\\mathbb{R}^d$ satisfying $\\mu(B(x,r)) \\le Cr^n$, $n \\in (0, d]$. The range of exponents in the Cotlar type inequality depend on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02950","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"}