{"paper":{"title":"Restriction of averaging operators to algebraic varieties over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Doowon Koh, Seongjun Yeom","submitted_at":"2016-01-28T07:55:01Z","abstract_excerpt":"We study $L^p\\to L^r$ estimates for restricted averaging operators related to algebraic varieties $V$ of $d$-dimensional vector spaces over finite fields $\\mathbb F_q$ with $q$ elements. We observe properties of both the Fourier restriction operator and the averaging operator over $V\\subset \\mathbb F_q^d.$ As a consequence, we obtain optimal results on the restricted averaging problems for spheres and paraboloids in dimensions $d\\ge2,$ and cones in odd dimensions $d\\ge 3.$ In addition, when the variety $V$ is a cone lying in an even dimensional vector space over $\\mathbb F_q$ and $-1$ is a squ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07677","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":""},"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"}