{"paper":{"title":"Fourier extension estimates on a strip in $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Aleksandar Bulj, Shobu Shiraki","submitted_at":"2025-08-28T06:29:22Z","abstract_excerpt":"Given a smooth curve with nonzero curvature $\\Sigma\\subset \\mathbb{R}^2$, let $E_{\\Sigma}$ denote the associated Fourier extension operator. For both general compact curves and the parabola, we characterize the pairs $(p,q)\\in [1,\\infty]^2$ for which the estimates $\\|E_{\\Sigma}f\\|_{L^q(\\Omega)}\\leq C\\|f\\|_{L^p(\\Sigma)}$ and $(\\mathcal{R}(|E_{\\Sigma}f|^{q}))^{\\frac{1}{q}}\\leq C\\|f\\|_{L^p(\\Sigma)}$ hold, where $\\Omega$ is a strip in $\\mathbb{R}^2$ and $\\mathcal{R}$ denotes the Radon transform. This work continues the study of mass concentration of $x\\mapsto E_{\\Sigma}f(x)$ near lines in $\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20463","kind":"arxiv","version":2},"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/2508.20463/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"}