{"paper":{"title":"Optimal estimates for harmonic functions in the unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Kalaj, Marijan Markovic","submitted_at":"2011-02-19T15:58:42Z","abstract_excerpt":"We find the sharp constants $C_p$ and the sharp functions $C_p=C_p(x)$ in the inequality $$|u(x)|\\leq \\frac{C_p}{(1-|x|^2)^{(n-1)/p}}\\|u\\|_{h^p(B^n)}, u\\in h^p(B^n), x\\in B^n,$$ in terms of Gauss hypergeometric and Euler functions. This extends and improves some results of Axler, Bourdon and Ramey (\\cite{ABR}), where they obtained similar results which are sharp only in the cases $p=2$ and $p=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3995","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"}