{"paper":{"title":"Inequalities for $L^p$-norms that sharpen the triangle inequality and complement Hanner's Inequality","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Elliott H. Lieb, Eric A. Carlen, Paata Ivanisvili, Rupert L. Frank","submitted_at":"2018-07-15T19:33:06Z","abstract_excerpt":"In 2006 Carbery raised a question about an improvement on the na\\\"ive norm inequality $\\|f+g\\|_p^p \\leq 2^{p-1}(\\|f\\|_p^p + \\|g\\|_p^p)$ for two functions in $L^p$ of any measure space. When $f=g$ this is an equality, but when the supports of $f$ and $g$ are disjoint the factor $2^{p-1}$ is not needed. Carbery's question concerns a proposed interpolation between the two situations for $p>2$. The interpolation parameter measuring the overlap is $\\|fg\\|_{p/2}$. We prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid for all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05599","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"}