{"paper":{"title":"A new proof of maximal theorem on Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"New proof shows the strong maximal operator is L^p bounded on Heisenberg groups with bound independent of dimension","cross_cats":[],"primary_cat":"math.CA","authors_text":"Chuhan Sun, Zipeng Wang","submitted_at":"2026-05-14T15:28:15Z","abstract_excerpt":"We give a new proof for the L^p-boundedness of the strong maximal operator defined on (2n+1)-dimensional real Heisenberg groups by using a geometric covering lemma due to Cordoba and Fefferman.\n  Furthermore, by considering the maximal operator defined over rectangles having only 3-parameter dilations, we show that the regarding L^p-norm inequality is independent of n. This is a consequence of Bourgain's dimension-free estimate on Hardy-Littlewood maximal function."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give a new proof for the L^p-boundedness of the strong maximal operator defined on (2n+1)-dimensional real Heisenberg groups by using a geometric covering lemma due to Cordoba and Fefferman. Furthermore... the regarding L^p-norm inequality is independent of n.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Cordoba-Fefferman geometric covering lemma applies directly to the adapted rectangles on the Heisenberg group without additional geometric adjustments that might depend on n.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New proof of L^p boundedness for the strong maximal operator on Heisenberg groups, plus dimension-free estimate for 3-parameter dilations via Bourgain's result.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"New proof shows the strong maximal operator is L^p bounded on Heisenberg groups with bound independent of dimension","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"22a01e8756abdbcd733ce5aeebaffca64a7e821b8701c2ce7e58be0928ca7f1e"},"source":{"id":"2605.14961","kind":"arxiv","version":1},"verdict":{"id":"f87244a6-2989-4d12-a59a-47585c479fc4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:44:49.651627Z","strongest_claim":"We give a new proof for the L^p-boundedness of the strong maximal operator defined on (2n+1)-dimensional real Heisenberg groups by using a geometric covering lemma due to Cordoba and Fefferman. Furthermore... the regarding L^p-norm inequality is independent of n.","one_line_summary":"New proof of L^p boundedness for the strong maximal operator on Heisenberg groups, plus dimension-free estimate for 3-parameter dilations via Bourgain's result.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Cordoba-Fefferman geometric covering lemma applies directly to the adapted rectangles on the Heisenberg group without additional geometric adjustments that might depend on n.","pith_extraction_headline":"New proof shows the strong maximal operator is L^p bounded on Heisenberg groups with bound independent of dimension"},"references":{"count":10,"sample":[{"doi":"","year":1986,"title":"Bourgain, On the ^p -bounds for maximal functions associated to convex bodies in ^n , Israel Journal of Mathematics, 54 : no.3, 257-265,1986","work_id":"d6e271c0-e251-4a03-b428-88fbfe57e2eb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Bourgain, On the Hardy-Littlewood maximal function for the cube , Israel Journal of Mathematics, 203 : no.1, 275-293, 2014","work_id":"52405476-187c-4124-bab1-15156b9e8925","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1975,"title":"C\\' o rdoba and R","work_id":"86b775d7-c616-4178-8a24-af8793edebbc","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"Christ, Hilbert transforms along curves","work_id":"b983781d-5573-4dff-9488-b0477dfc5ab6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1992,"title":"Christ, The strong maximal function on a nilpotent group , Transactions of the American Mathematical Society 331 : no.1, 1-13, 1992","work_id":"c4c7ba6d-6099-4967-a928-809cc5670267","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":10,"snapshot_sha256":"9311d82cb7867295094f88d7563b48135f2c9b36453f854bb5eb54e740df526c","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2b353af2aa9f14d59a6187f8ec6ea21be83da4e94d67220e0efafec77a493706"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}