{"paper":{"title":"Weighted Hardy Inequality in $l_2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ivan Gadjev","submitted_at":"2026-06-08T05:46:21Z","abstract_excerpt":"We study the behaviour of the smallest possible constant $d_n$ in weighted Hardy inequality $$ \\sum_{k=1}^{n}\\Big(\\frac{1}{k}\\sum_{j=1}^{k}a_j\\Big)^2 k^\\epsilon\\le d(n,\\epsilon)\\,\\sum_{k=1}^{n}{a_k^2}\\,k^\\epsilon $$ The exact rate of convergence of $d_n$ is established and the ``almost extremal'' sequence is found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09057","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/2606.09057/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"}