{"paper":{"title":"Pisier's inequality revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Assaf Naor, Tuomas Hyt\\\"onen","submitted_at":"2012-07-23T12:55:21Z","abstract_excerpt":"Given a Banach space $X$, for $n\\in \\mathbb N$ and $p\\in (1,\\infty)$ we investigate the smallest constant $\\mathfrak P\\in (0,\\infty)$ for which every $f_1,...,f_n:{-1,1}^n\\to X$ satisfy \\int_{{-1,1}^n}\\Bigg|\\sum_{j=1}^n \\partial_jf_j(\\varepsilon)\\Bigg|^pd\\mu(\\varepsilon) \\leq \\mathfrak{P}^p\\int_{{-1,1}^n}\\int_{{-1,1}^n}\\Bigg\\|\\sum_{j=1}^n \\d_j\\Delta f_j(\\varepsilon)\\Bigg\\|^pd\\mu(\\varepsilon) d\\mu(\\delta), where $\\mu$ is the uniform probability measure on the discrete hypercube ${-1,1}^n$ and ${\\partial_j}_{j=1}^n$ and $\\Delta=\\sum_{j=1}^n\\partial_j$ are the hypercube partial derivatives and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5375","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"}