{"paper":{"title":"Composition operators on generalized Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Elodie Pozzi, Emmanuel Russ (IF), Juliette Leblond (INRIA Sophia Antipolis), Sam Elliott","submitted_at":"2013-10-16T04:31:53Z","abstract_excerpt":"Let $\\Omega_1,\\Omega_2\\subset {\\mathbb C}$ be bounded domains. Let $\\phi:\\Omega_1\\rightarrow \\Omega_2$ holomorphic in $\\Omega_1$ and belonging to $W^{1,\\infty}_{\\Omega_2}(\\Omega_1)$. We study the composition operators $f\\mapsto f\\circ\\phi$ on generalized Hardy spaces on $\\Omega_2$, recently considered in \\cite{bfl, BLRR}. In particular, we provide necessary and/or sufficient conditions on $\\phi$, depending on the geometry of the domains, ensuring that these operators are bounded, invertible, isometric or compact. Some of our results are new even for Hardy spaces of analytic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4268","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"}