{"paper":{"title":"Sharp bounds for the $\\boldsymbol{p}$-adic $\\boldsymbol{n}$-dimensional fractional Hardy operator and a class of integral operators on $\\boldsymbol{p}$-adic function spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tianyang He, Ting Yu, Zhiwen Liu","submitted_at":"2025-04-27T15:13:55Z","abstract_excerpt":"In this paper, we first study the sharp weak estimate for the $p$-adic $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\\infty}$. Secondly, we study the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator with a kernel on $p$-adic weighted spaces $H_{\\alpha}^{\\infty}( \\mathbb{Q} _{p}^{n} )$. As an application, the sharp bounds for $p$-adic Hardy and Hilbert operators on $p$-adic weighted spaces are obtained. Finally, we also find the sharp bound for the Hausdorff operator on $p$-adic weighted spaces, which generalizes the previous results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19273","kind":"arxiv","version":2},"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/2504.19273/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"}