{"paper":{"title":"Musielak-Orlicz Spaces that are Isomorphic to Subspaces of L_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Joscha Prochno","submitted_at":"2012-04-26T19:57:44Z","abstract_excerpt":"In this note we prove that $\\frac{1}{n!} \\sum_{\\pi} (\\sum_{i=1}^n |x_i a_{i,\\pi(i)} |^2)^{1/2}$ is equivalent to a Musielak-Orlicz norm $\\norm{x}_{\\sum M_i}$. We also obtain the inverse result, i.e., given the Orlicz functions, we provide a formula for the choice of the matrix that generates the corresponding Musielak-Orlicz norm. As a consequence, we obtain the embedding of 2-concave Musielak-Orlicz spaces into L_1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6030","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"}