{"paper":{"title":"Mixed Bohr radius in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Daniel Galicer, Mart\\'in Mansilla, Santiago Muro","submitted_at":"2017-12-21T16:50:17Z","abstract_excerpt":"Let $K(B_{\\ell_p^n},B_{\\ell_q^n}) $ be the $n$-dimensional $(p,q)$-Bohr radius for holomorphic functions on $\\mathbb C^n$. That is, $K(B_{\\ell_p^n},B_{\\ell_q^n}) $ denotes the greatest constant $r\\geq 0$ such that for every entire function $f(z)=\\sum_{\\alpha} c_{\\alpha} z^{\\alpha}$ in $n$-complex variables, we have the following (mixed) Bohr-type inequality $$\\sup_{z \\in r \\cdot B_{\\ell_q^n}} \\sum_{\\alpha} | c_{\\alpha} z^{\\alpha} | \\leq \\sup_{z \\in B_{\\ell_p^n}} | f(z) |,$$ where $B_{\\ell_r^n}$ denotes the closed unit ball of the $n$-dimensional sequence space $\\ell_r^n$.\n  For every $1 \\leq p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08077","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"}