{"paper":{"title":"Hessian of Bellman functions and uniqueness of Brascamp--Lieb inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"A. Volberg, P. Ivanisvili","submitted_at":"2014-11-19T20:28:02Z","abstract_excerpt":"Under some assumptions on the vectors $a_{1},..,a_{n} \\in\\mathbb{R}^{k}$ and the function $B : \\mathbb{R}^{n} \\to \\mathbb{R}$ we find the sharp estimate of the expression $\\int_{\\mathbb{R}^{k}} B(u_{1}(a_{1}\\cdot x),..., u_{n}(a_{n}\\cdot x))dx$ in terms of $\\int_{\\mathbb{R}}u_{j}(y)dy, j=1,...,n.$ In some particular case we will show that these assumptions on $B$ imply that there is only one Brascamp--Lieb inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5349","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"}