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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","authors_text":"Albin Petersson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-05-27T20:58:47Z","title":"Trace type Orlicz spaces and analysis of Orlicz spaces by Lebesgue exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21764","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:826007efbfb06a346b4c0c02df880fff9d4480ee0abfb6d8365722b5899897c5","target":"record","created_at":"2026-07-05T11:31:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ac3b1298d8b9caabc0990713bb1854f8ba346cc2e0095ad063aa5c3e3656e68c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-05-27T20:58:47Z","title_canon_sha256":"485d2681466d2a329318793459a92728e47d99cca2b019a1d42461c1beaa3b5e"},"schema_version":"1.0","source":{"id":"2505.21764","kind":"arxiv","version":2}},"canonical_sha256":"ace32f042d72f201db54e99c9dd1993b83b34f6e16c757a99d9d92ed4de54d53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ace32f042d72f201db54e99c9dd1993b83b34f6e16c757a99d9d92ed4de54d53","first_computed_at":"2026-07-05T11:31:45.730580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:45.730580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hPr9yxtCy8GOUfkiqTjKXuJX7LgTzmCAw+VvofYKJWk8OkartV1ab9yxVbI/+xDaXX+uLoS9Q8+rsd5/ZGEvDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:45.731146Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21764","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:826007efbfb06a346b4c0c02df880fff9d4480ee0abfb6d8365722b5899897c5","sha256:7fb12e28f7eec5560f77c21e4c8bb0e7d36ebfb82857a35b5d999f601ba3f04d"],"state_sha256":"12b3b7a5c5d82026a9087a9e7960199a3131b94ad53d795fced7a00bcf2884a7"}