{"paper":{"title":"On the Constant and Extremal Function for Weighted Hardy Inequality in $L_p$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ivan Gadjev","submitted_at":"2026-06-08T06:03:23Z","abstract_excerpt":"We study the behaviour of the smallest possible constant $d(a,b, p,\\epsilon)$ in Hardy inequality $$ \\int_a^b\\left(\\frac{1}{x}\\int_a^xf(t)dt\\right)^px^{\\epsilon}\\,dx\\leq d(a,b,p,\\epsilon)\\,\\int_a^b [f(x)]^px^{\\epsilon}\\, dx, \\quad 2\\le p<\\infty. $$ The exact rate of convergence of $d(a,b,p,\\epsilon)$ is established and the ``almost extremal'' function is found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09067","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/2606.09067/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"}