{"paper":{"title":"Embedding and compact embedding between Bergman and Hardy spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Fugang Yan, Guanlong Bao, Kehe Zhu, Pan Ma","submitted_at":"2025-02-12T13:48:35Z","abstract_excerpt":"For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\\mathbb C}^n$, we determine exactly when $A^p_\\alpha\\subset H^q$ or $H^p\\subset A^q_\\alpha$, where $0<q<\\infty$, $0<p<\\infty$, and $-\\infty<\\alpha<\\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08406","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.08406/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}