{"paper":{"title":"Knapp-type obstructions in multilinear fractal Fourier extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.CA","authors_text":"Ana E. de Orellana, Itamar Oliveira","submitted_at":"2026-02-09T12:06:42Z","abstract_excerpt":"For curved, smooth hypersurfaces, the classical Knapp example shows that the Stein--Tomas theorem, which gives linear Fourier restriction estimates, is sharp. Variants of this example combined with the geometric notion of \\textit{transversality} motivate the $L^{2}$-based multilinear Fourier extension conjecture. In the fractal setting, work by Mockenhaupt, Mitsis, and Bak-Seeger extended the linear Fourier restriction estimate beyond the smooth setting, and subsequent work showed this extension to be sharp. In this article, we construct multilinear Knapp-type examples for fractal measures ins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.08568","kind":"arxiv","version":3},"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/2602.08568/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"}