{"paper":{"title":"The sup-norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Galicer, Mart\\'in Mansilla, Santiago Muro","submitted_at":"2016-02-04T16:34:41Z","abstract_excerpt":"Let $A_{p,r}^m(n)$ be the best constant that fulfills the following inequality: for every $m$-homogeneous polynomial $P(z) = \\sum_{|\\alpha|=m} a_{\\alpha} z^{\\alpha}$ in $n$ complex variables, $$\\big( \\sum_{|\\alpha|=m} |a_{\\alpha}|^{r} \\big)^{1/r} \\leq A_{p,r}^m(n) \\sup_{z \\in B_{\\ell_p^n}} \\big|P(z) \\big| .$$ For every degree $m$, and a wide range of values of $ p,r \\in [1,\\infty]$ (including any $r$ in the case $p \\in [1,2]$, and any $r$ and $p$ for the 2-homogeneous case), we give the correct asymptotic behavior of these constants as $n$ (the number of variables) tends to infinity. Remarkabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01735","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"}