{"paper":{"title":"Lower bounds for the complex polynomial Hardy--Littlewood inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Gustavo Araujo","submitted_at":"2014-10-12T00:12:01Z","abstract_excerpt":"The Hardy--Littlewood inequality for complex homogeneous polynomials asserts that given positive integers $m\\geq2$ and $n\\geq1$, if $P$ is a complex homogeneous polynomial of degree $m$ on $\\ell_{p}^{n}$ with $2m\\leq p\\leq\\infty$ given by $P(x_{1},\\ldots,x_{n})=\\sum_{|\\alpha|=m}a_{\\alpha }\\mathbf{{x}^{\\alpha}}$, then there exists a constant $C_{\\mathbb{C},m,p}^{\\mathrm{pol}}\\geq1$ (which is does not depend on $n$) such that \\[ \\left( {\\sum\\limits_{\\left\\vert \\alpha\\right\\vert =m}}\\left\\vert a_{\\alpha }\\right\\vert ^{\\frac{2mp}{mp+p-2m}}\\right) ^{\\frac{mp+p-2m}{2mp}}\\leq C_{\\mathbb{C},m,p}^{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3037","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"}