{"paper":{"title":"L^p regularity of averages over curves and bounds for associated maximal operators","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Malabika Pramanik","submitted_at":"2005-01-11T16:49:18Z","abstract_excerpt":"We prove that for a finite type curve in $\\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \\to L^{p}_{1/p}$ regularity result for the averaging operators for large $p$. The proofs make use of a deep result of Thomas Wolff about decompositions of cone multipliers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501165","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/math/0501165/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"}