{"paper":{"title":"On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Gustavo Araujo","submitted_at":"2014-07-26T11:02:21Z","abstract_excerpt":"In this paper, among other results, we improve the best known estimates for the constants of the generalized Bohnenblust-Hille inequality. These enhancements are then used to improve the best known constants of the Hardy--Littlewood inequality; this inequality asserts that for a positive integer $m\\geq2$ with $2m\\leq p\\leq\\infty$ and $\\mathbb{K}=\\mathbb{R}$ or $\\mathbb{C}$ there exists a constant $C_{m,p}^{\\mathbb{K}}\\geq1$ such that, for all continuous $m$--linear forms $T:\\ell_{p}^{n}\\times\\cdots\\times\\ell_{p}^{n}\\rightarrow\\mathbb{K}$, and all positive integers $n$,% \\[ \\left( \\sum_{j_{1},."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7120","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"}