{"paper":{"title":"$l^p$ decoupling for restricted $k$-broadness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xiaochun Li, Xiumin Du","submitted_at":"2016-11-09T00:21:04Z","abstract_excerpt":"To prove Fourier restriction estimate using polynomial partitioning, Guth introduced the concept of $k$-broad part of regular $L^p$ norm and obtained sharp $k$-broad restriction estimates. To go from $k$-broad estimates to regular $L^p$ estimates, Guth employed $l^2$ decoupling result. In this article, similar to the technique introduced by Bourgain-Guth, we establish an analogue to go from regular $L^p$ norm to its $(m+1)$-broad part, as the error terms we have the restricted $k$-broad parts ($k=2,\\cdots,m$). To analyze the restricted $k$-broadness, we prove an $l^p$ decoupling result, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02781","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":""},"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"}