{"paper":{"title":"Decoupling and near-optimal restriction estimates for Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hong Wang, Izabella Laba","submitted_at":"2016-07-28T03:16:26Z","abstract_excerpt":"For any $\\alpha\\in(0,d)$, we construct Cantor sets in $\\mathbb{R}^d$ of Hausdorff dimension $\\alpha$ such that the associated natural measure $\\mu$ obeys the restriction estimate $\\| \\widehat{f d\\mu} \\|_{p} \\leq C_p \\| f \\|_{L^2(\\mu)}$ for all $p>2d/\\alpha$. This range is optimal except for the endpoint. This extends the earlier work of Chen-Seeger and Shmerkin-Suomala, where a similar result was obtained by different methods for $\\alpha=d/k$ with $k\\in\\mathbb{N}$. Our proof is based on the decoupling techniques of Bourgain-Demeter and a theorem of Bourgain on the existence of $\\Lambda(p)$ set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08302","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":""},"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"}