{"paper":{"title":"Lower bounds for the constants of the 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":"2014-05-12T21:35:47Z","abstract_excerpt":"Given an integer $m\\geq2$, the Hardy--Littlewood inequality (for real scalars) says that for all $2m\\leq p\\leq\\infty$, there exists a constant $C_{m,p}% ^{\\mathbb{R}}\\geq1$ such that, for all continuous $m$--linear forms $A:\\ell_{p}^{N}\\times\\cdots\\times\\ell_{p}^{N}\\rightarrow\\mathbb{R}$ and all positive integers $N$, \\[ \\left( \\sum_{j_{1},...,j_{m}=1}^{N}\\left\\vert A(e_{j_{1}},...,e_{j_{m}% })\\right\\vert ^{\\frac{2mp}{mp+p-2m}}\\right) ^{\\frac{mp+p-2m}{2mp}}\\leq C_{m,p}^{\\mathbb{R}}\\left\\Vert A\\right\\Vert . \\] The limiting case $p=\\infty$ is the well-known Bohnenblust--Hille inequality; the beh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2969","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"}