{"paper":{"title":"Reverse Holder inequalities revisited: Interpolation, Extrapolation, Indices and Doubling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alvaro Corval\\'an, Mario Milman","submitted_at":"2019-07-25T22:35:22Z","abstract_excerpt":"Extending results in \\cite{M} and \\cite{MM} we characterize the classical classes of weights that satisfy reverse H\\\"{o}lder inequalities in terms of indices of suitable families of $K-$functionals of the weights. In particular, we introduce a Samko type of index (cf. \\cite{kara}) for families of functions, that is based on quasi-monotonicity, and use it to provide an index characterization of the $RH_{p}$ classes, as well as the limiting class $RH=$ $RH_{LLogL}=$. $\\bigcup\\limits_{p>1}RH_{p}$ (cf. \\cite{BMR}),\\ which in the abstract case involves extrapolation spaces. Reverse H\\\"{o}lder inequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11327","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"}