{"paper":{"title":"Weighted Bergman spaces induced by rapidly incresing weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2012-10-11T18:09:00Z","abstract_excerpt":"This monograph is devoted to the study of the weighted Bergman space $A^p_\\om$ of the unit disc $\\D$ that is induced by a radial continuous weight $\\om$ satisfying\n  {equation}\\label{absteq}\n  \\lim_{r\\to\n  1^-}\\frac{\\int_r^1\\om(s)\\,ds}{\\om(r)(1-r)}=\\infty.\\tag{\\dag}\n  {equation} Every such $A^p_\\om$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\\a$. Even if it is well known that $H^p$ is the limit of $A^p_\\a$, as $\\a\\to-1$, in many respects, it is shown that $A^p_\\om$ lies \"closer\" to $H^p$ than any $A^p_\\a$, and that several finer function-theoretic proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3311","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"}