{"paper":{"title":"Improving Beckner's bound via Hermite functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Paata Ivanisvili","submitted_at":"2016-06-27T22:20:02Z","abstract_excerpt":"We obtain an improvement of the Beckner's inequality $\\| f\\|^{2}_{2} -\\|f\\|^{2}_{p} \\leq (2-p) \\| \\nabla f\\|_{2}^{2}$ valid for $p \\in [1,2]$ and the Gaussian measure. Our improvement is essential for the intermediate case $p \\in (1,2)$, and moreover, we find the natural extension of the inequality for any real $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08500","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"}