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We characterize validity of the inequality\n  \\[\n  \\left(\\int_0^\\infty w(t) (f^*(t))^q \\, dt \\right)^\\frac 1q \\le C \\left(\\int_0^\\infty v(t) \\left(\\int_t^\\infty u(s) (f^*(s))^m \\,ds \\right)^\\frac pm \\! dt \\right)^\\frac 1p\n  \\] for all measurable functions $f$ defined on $\\mathbb{R}^n$ and provide equivalent estimates of the optimal constant $C>0$ in terms of the weights and exponents. The obtained conditions characterize the embedding of the Copson-Lorentz space $CL^{m,p}(u,v)$, generated by the functional\n  \\[\n  \\|f\\|_{{CL^{m,p}("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.03725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-12T14:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"2e4dbb5e65d774fe21057e7724206d412bb2973b00c6ba5ac5f4b9ae76805571","abstract_canon_sha256":"6137f2eebad5f9434de7dae9d3fc5af47c6b128eab5d025af8549c789dfdcab3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:41.881334Z","signature_b64":"Ul8D6TNMYAi04sjXER3GDQr34e/+d/FaU/QgO/huKvp7oFbVrjvBSlyUT4xLkvOUiAHxrmBRXd6dgtKhA/CiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6765590f1617a2de7dcf00e9932c8c4e56fbe87d47910f79e42117935afef19","last_reissued_at":"2026-05-18T00:03:41.880870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:41.880870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embeddings and associated spaces of Copson-Lorentz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Martin K\\v{r}epela","submitted_at":"2016-12-12T14:57:29Z","abstract_excerpt":"Let $m,p,q\\in(0,\\infty)$ and let $u,v,w$ be nonnegative weights. We characterize validity of the inequality\n  \\[\n  \\left(\\int_0^\\infty w(t) (f^*(t))^q \\, dt \\right)^\\frac 1q \\le C \\left(\\int_0^\\infty v(t) \\left(\\int_t^\\infty u(s) (f^*(s))^m \\,ds \\right)^\\frac pm \\! dt \\right)^\\frac 1p\n  \\] for all measurable functions $f$ defined on $\\mathbb{R}^n$ and provide equivalent estimates of the optimal constant $C>0$ in terms of the weights and exponents. 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