{"paper":{"title":"Optimal Weak Parallelogram Constants for $L^p$ Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javad Mashreghi, Raymond Cheng, William T. Ross","submitted_at":"2018-02-13T14:48:33Z","abstract_excerpt":"Inspired by Clarkson's inequalities for $L^p$ and continuing work from \\cite{CR}, this paper computes the optimal constant $C$ in the weak parallelogram laws $$ \\|f + g \\|^r + C\\|f - g\\|^r \\leq 2^{r-1}\\big( \\|f\\|^r + \\|g\\|^r \\big), $$ $$ \\|f + g \\|^r + C\\|f- g \\|^r \\geq 2^{r-1}\\big( \\|f\\|^r + \\|g \\|^r \\big)$$ for the $L^p$ spaces, $1 < p < \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04649","kind":"arxiv","version":1},"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"}