{"paper":{"title":"Weighted Hardy Inequalities for Nested Averages","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ludovick Bouthat, Pierre-Olivier Paris\\'e","submitted_at":"2026-06-23T01:05:03Z","abstract_excerpt":"We study a family of Hardy-type inequalities for weighted averages over nested subsets of a measure space. Given a partition of a measure space and a weight function $m$, we consider operators of the form \\[ f \\mapsto \\frac{1}{M_n}\\int_{X^{(n)}} m(x)f(x)\\,\\mathrm{d}\\mu(x), \\] with additional weights on the resulting sequence of averages. In particular, we generalize an inequality obtained by Vincent and Sohani in \\cite{VincentSohani2025} and characterize the boundedness in terms of the finiteness of a single testing quantity $\\beta$. We also provide two-sided estimates for the best constant $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24044","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}