{"paper":{"title":"On the resonant Carleson-Radon transform in all dimensions. The degree one resonant case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.CA","authors_text":"Martin Hsu, Victor Lie","submitted_at":"2026-06-25T16:07:54Z","abstract_excerpt":"In this paper, we provide the resolution of the degree one resonant case in all dimensions.\n  Our main result reads as follows: for any dimension $D\\geq 1$ set $\\mathbf{X}(\\mathbf{t})=(\\mathbf{t},|\\mathbf{t}|^2),\\; \\mathbf{t}\\in\\mathbb{R}^D$, and let $K(\\mathbf{t})$ be any suitable translation invariant Calder\\'on--Zygmund kernel. If $\\mathbb{V}\\leq\\mathbb{R}^{D+1}$ is any linear subspace such that $ \\exists\\:\\:\\mathbf{v}_0\\in\\mathbb{R}^D\\times\\{0\\}$ nontrivial with $\\mathbf{v}_0\\perp\\mathbb{V}$ then the following (maximal) Carleson-Radon transform $CR^\\ast_{\\mathbb{V}}$ is $L^p(\\mathbb{R}^{D+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27219","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/2606.27219/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"}