{"paper":{"title":"On a Carleson-Radon Transform (the non-resonant setting)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Martin Hsu, Victor Lie","submitted_at":"2024-11-03T19:10:48Z","abstract_excerpt":"Given a curve $\\vec{\\gamma}=(t^{\\alpha_1}, t^{\\alpha_2}, t^{\\alpha_3})$ with $\\vec{\\alpha}=(\\alpha_1,\\alpha_2,\\alpha_3)\\in \\mathbb{R}_{+}^3$, we define the Carleson-Radon transform along $\\vec{\\gamma}$ by the formula $$ C_{[\\vec{\\alpha}]}f(x,y):=\\sup_{a\\in \\mathbb{R}}\\left|p.v.\\,\\int_{\\mathbb{R}} f (x-t^{\\alpha_1},y-t^{\\alpha_2})\\,e^{i\\,a\\,t^{\\alpha_3}}\\,\\frac{dt}{t}\\right|\\,.$$ We show that in the \\emph{non-resonant} case, that is, when the coordinates of $\\vec{\\alpha}$ are pairwise disjoint, our operator $ C_{[\\vec{\\alpha}]}$ is $L^p$ bounded for any $1<p<\\infty$. Our proof relies on the (Ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01660","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/2411.01660/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"}