{"paper":{"title":"On the embedding of 2-concave Orlicz spaces into $L^1$","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carsten Sch\\\"utt","submitted_at":"1994-02-01T16:01:49Z","abstract_excerpt":"In [K--S 1] it was shown that\n  $$ \\underset {\\pi} \\to {\\text{Ave}} (\\sum_{i=1}^{n}|x_i a_{\\pi(i)}|^2)^{\\frac {1}{2}} $$\n  is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence $a_1, a_2,....,a_n$ so that the above expression is equivalent to a given Orlicz norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9402204","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"}