{"paper":{"title":"Lacunary elliptic maximal operator on the Heisenberg group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeongtae Oh, Joonil Kim","submitted_at":"2025-01-21T07:05:05Z","abstract_excerpt":"In this paper, we prove \\( L^p \\) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \\( L^p \\) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group operations, to arbitrary matrices \\( A \\), investigating how the curvature induced by \\( A \\) governs the \\( L^p \\) boundedness of lacunary circular and elliptic maximal operators. Specifically, we provide necessary and sufficient conditions on \\( A \\) that determine whether these operators are bounded or unbounded on \\( L^p \\)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11928","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/2501.11928/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"}