{"paper":{"title":"Uniform Sobolev inequalities for second order non-elliptic differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eunhee Jeong, Sanghyuk Lee, Yehyun Kwon","submitted_at":"2015-10-20T02:45:33Z","abstract_excerpt":"We study uniform Sobolev inequalities for the second order differential operators $P(D)$ of non-elliptic type. For $d\\ge3$ we prove that the Sobolev type estimate $\\|u\\|_{L^q(\\mathbb{R}^d)}\\le C \\|P(D)u\\|_{L^p(\\mathbb{R}^d)}$ holds with $C$ independent of the first order and the constant terms of $P(D)$ if and only if $1/p-1/q=2/d$ and $\\frac{2d(d-1)}{d^2+2d-4}<p<\\frac{2(d-1)}d$. We also obtain restricted weak type endpoint estimates for the critical $(p,q)=(\\frac{2(d-1)}{d},\\frac{2d(d-1)}{(d-2)^2})$, $(\\frac{2d(d-1)}{d^2+2d-4}, \\frac{2(d-1)}{d-2})$. As a consequence, the result extends the cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05741","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"}