{"paper":{"title":"Weak A_\\infty weights and weak Reverse H\\\"older property in a space of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Olli Tapiola, Theresa C. Anderson, Tuomas Hyt\\\"onen","submitted_at":"2014-10-14T08:22:37Z","abstract_excerpt":"In the Euclidean setting, the Fujii-Wilson-type $A_\\infty$ weights satisfy a Reverse H\\\"older Inequality (RHI) but in spaces of homogeneous type the best known result has been that $A_\\infty$ weights satisfy only a weak Reverse H\\\"older Inequality. In this paper, we compliment the results of Hyt\\\"onen, P\\'erez and Rela and show that there exist both $A_\\infty$ weights that do not satisfy an RHI and a genuinely weaker weight class that still satisfies a weak RHI. We also show that all the weights that satisfy a weak RHI have a self-improving property but the self-improving property of the stron"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3608","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"}