{"paper":{"title":"Trace type Orlicz spaces and analysis of Orlicz spaces by Lebesgue exponents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Albin Petersson","submitted_at":"2025-05-27T20:58:47Z","abstract_excerpt":"In the paper, we analyze the Lebesgue exponents $p_\\Phi$ and $q_\\Phi$, and show that for any $p_\\Phi< p < \\infty$ and $1< q<q_\\Phi$, there exists an equivalent Young function $\\Psi$ with $p < p_\\Psi < \\infty$ and $1<q_\\Psi < q$. This type of construction is used to improve upon the inclusions $L^{p_\\Phi}\\cap L^{q_\\Phi}\\subseteq L^\\Phi \\subseteq L^{p_\\Phi} + L^{q_\\Phi}$. For trace type Orlicz spaces $L^{\\Phi,\\Phi}$, we find that when $\\Phi \\in \\Delta_2$, we have $L^{\\Phi,\\Phi} \\subseteq L^\\Phi$ if and only if $\\Phi(||f||_{L^\\Phi}) \\le C \\rho_\\Phi(f)$ for all $f\\in L^\\Phi$, and the reverse inclu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21764","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21764/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"}