{"paper":{"title":"Optimal comparison of $P$-norms of Dirichlet Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Andreas Defant, Antonio P\\'erez","submitted_at":"2016-03-07T16:07:04Z","abstract_excerpt":"Let $1 \\leq p < q < \\infty$. We show that \\[ \\sup{\\frac{\\left\\| D\\right\\|_{\\mathcal{H}_{q}}}{\\left\\| D\\right\\|_{\\mathcal{H}_{p}}}} = \\exp{\\left( \\frac{\\log{x}}{\\log{\\log{x}}} \\left(\\log{\\sqrt{\\frac{q}{p}}} + \\left(\\frac{\\log{\\log{\\log{x}}}}{\\log{\\log{x}}}\\right)\\right) \\right)} \\,,\\] where the supremum is taken over all non-zero Dirichlet polynomials of the form $D(s)=\\sum_{n \\leq x}{a_{n} n^{-s}}$. An aplication is given to the study of multipliers between Hardy spaces of Dirichlet series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02128","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"}