{"paper":{"title":"Sharp Estimates for $p$-Adic Hardy, Hardy-Littlewood-P\\'olya Operators and Commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Qingyan Wu, Shanzhen Lu, Zunwei Fu","submitted_at":"2011-05-14T11:12:09Z","abstract_excerpt":"In this paper we get the sharp estimates of the $p$-adic Hardy and Hardy-Littlewood-P\\'olya operators on $L^q(|x|^{\\alpha}_pdx)$. Also, we prove that the commutators generated by the $p$-adic Hardy operators (Hardy-Littlewood-P\\'olya operators) and the central BMO functions are bounded on $L^q(|x|^{\\alpha}_pdx)$, more generally, on Herz spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2888","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"}