{"paper":{"title":"Improving bounds for singular operators via Sharp Reverse H\\\"older Inequality for $A_{\\infty}$","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":"2012-04-07T18:20:46Z","abstract_excerpt":"In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse H\\\"older Inequality for $A_{\\infty}$ weights. For two given operators $T$ and $S$, we study $L^p(w)$ bounds of Coifman-Fefferman type. $ \\|Tf\\|_{L^p(w)}\\le c_{n,w,p} \\|Sf\\|_{L^p(w)}, $ that can be understood as a way to control $T$ by $S$. We will focus on a \\emph{quantitative} analysis of the constants involved and show that we can improve classical results regarding the dependence on the weight $w$ in terms of Wilson's $A_{\\infty}$ constant $ [w]_{A_{\\infty}}:=\\sup_Q\\frac{1}{w(Q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1667","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"}