{"paper":{"title":"Remarks on the Hardy--Littlewood inequality for $m$-homogeneous polynomials and $m$-linear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. Nunez-Alarcon, D. Pellegrino, W. Cavalcante","submitted_at":"2015-07-22T08:32:49Z","abstract_excerpt":"The Hardy--Littlewood inequality for $m$-homogeneous polynomials on $\\ell_{p}$ spaces is valid for $p>m.$ In this note, among other results, we present an optimal version of this inequality for the case $p=m.$ We also show that the optimal constant, when restricted to the case of $2$-homogeneous polynomials on $\\ell_{2}(\\mathbb{R}^{2})$ is precisely $2$. In an Appendix we justify why, curiously, the optimal exponents of the Hardy--Littlewood inequality do not behave smoothly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06099","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"}