{"paper":{"title":"A Bernstein-type inequality for rational functions in weighted Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anton Baranov, Rachid Zarouf (LATP)","submitted_at":"2010-03-26T08:03:07Z","abstract_excerpt":"Given $n\\geq1$ and $r\\in[0, 1),$ we consider the set $\\mathcal{R}_{n, r}$ of rational functions having at most $n$ poles all outside of $\\frac{1}{r}\\mathbb{D},$ were $\\mathbb{D}$ is the unit disc of the complex plane. We give an asymptotically sharp Bernstein-type inequality for functions in $\\mathcal{R}_{n, r}\\:$ (as n tends to infinity and r tends to 1-) in weighted Bergman spaces with \"polynomially\" decreasing weights. We also prove that this result can not be extended to weighted Bergman spaces with \"super-polynomially\" decreasing weights."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5066","kind":"arxiv","version":4},"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"}