{"paper":{"title":"Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Li (LML)","submitted_at":"2010-10-29T13:52:11Z","abstract_excerpt":"It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \\leq p < \\infty$, is also compact on the Bergman space ${\\mathfrak B}^p = L^p_a (\\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^\\Psi$ and Bergman-Orlicz ${\\mathfrak B}^\\Psi$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^\\Psi$ but not on ${\\mathfrak B}^\\Psi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6207","kind":"arxiv","version":2},"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"}