{"paper":{"title":"Korenblum-Type Extremal Problems in Bergman Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexander Solynin, Pritha Chakraborty","submitted_at":"2015-07-22T23:27:16Z","abstract_excerpt":"We shall study non-linear extremal problems in Bergman space $\\mathcal{A}^2(\\mathbb{D})$. We show the existence of the solution and that the extremal functions are bounded. Further, we shall discuss special cases for polynomials, investigate the properties of the solution and provide a bound for the solution. This problem is an equivalent formulation of B. Korenblum's conjecture, also known as Korenblum's Maximum Principle: for $f$, $g\\in \\mathcal{A}^2(\\mathbb{D})$, there is a constant $c$, $0<c<1$ such that if $|f(z)|\\leq |g(z)|$ for all $z$ such that $c<|z|<1$, then $\\|f\\|_2\\leq \\|g\\|_2$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06356","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"}