{"paper":{"title":"Lorentz spaces with variable exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Henning Kempka, Jan Vyb\\'iral","submitted_at":"2012-10-05T12:43:05Z","abstract_excerpt":"We introduce Lorentz spaces $L_{p(\\cdot),q}(\\R^n)$ and $L_{p(\\cdot),q(\\cdot)}(\\R^n)$ with variable exponents. We prove several basic properties of these spaces including embeddings and the identity $L_{p(\\cdot),p(\\cdot)}(\\R^n)=L_{p(\\cdot)}(\\R^n)$. We also show that these spaces arise through real interpolation between $L_{\\p}(\\R^n)$ and $L_\\infty(\\R^n)$. Furthermore, we answer in a negative way the question posed in Diening, H\\\"ast\\\"o, and Nekvinda (2004) whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1738","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"}