{"paper":{"title":"Compact composition operators on Hardy-Orlicz and weighted Bergman-Orlicz spaces on the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"St\\'ephane Charpentier","submitted_at":"2011-01-19T12:34:10Z","abstract_excerpt":"Using recent characterizations of the compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball, we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H^{\\infty}. Then, we prove that, for each Koranyi region \\Gamma, there exists a map \\phi taking the ball into \\Gamma such that, C_{\\phi} is not compact on H^{\\psi}\\left(\\mathbb{B}_{N}\\right), when \\psi grows fast. Finally, we give another characterization of the compactness of composition operator on weighted Bergman-Orlicz spaces in terms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3677","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"}