{"paper":{"title":"Sharp estimates involving $A_\\infty$ and $LlogL$ constants, and their applications to PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alexander Reznikov, Oleksandra Beznosova","submitted_at":"2011-07-10T19:24:18Z","abstract_excerpt":"It is a well known fact that the union of the Reverse H\\\"{o}lder classes coincides with the union of the Muckenhoupt classes $A_p$, but the $A_\\infty$ constant of the weight $w$, which is a limit of its $A_p$ constants, is not a natural characterization for the weight in Reverse H\\\"{o}lder classes. We introduce the $RH_1$ condition as a limiting case of the $RH_p$ inequalities as $p$ tends to 1. Then we show sharp bound on $RH_1$ constant of the weight $w$ in terms of its $A_\\infty$ constant (from above and from below). We also prove the sharp version of the Gehring theorem for the case $p=1$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1885","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"}