{"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. 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}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03725","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"}