{"paper":{"title":"Franke-Jawerth embeddings for Besov and Triebel-Lizorkin spaces with variable exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Helena F. Gon\\c{c}alves, Henning Kempka, Jan Vyb\\'iral","submitted_at":"2016-11-28T05:25:52Z","abstract_excerpt":"The classical Jawerth and Franke embeddings $$ F^{s_0}_{p_0,q}({\\mathbb R}^n)\\hookrightarrow B^{s_1}_{p_1,p_0}({\\mathbb R}^n) \\quad \\mbox{and} \\quad B^{s_0}_{p_0,p_1}({\\mathbb R}^n)\\hookrightarrow F^{s_1}_{p_1,q}({\\mathbb R}^n) $$ are versions of Sobolev embedding between the scales of Besov and Triebel-Lizorkin function spaces for $s_0>s_1$ and $$ s_0-\\frac{n}{p_0} = s_1-\\frac{n}{p_1}.$$ We prove Jawerth and Franke embeddings for the scales of Besov and Triebel-Lizorkin spaces with all exponents variable $$ F^{s_0(\\cdot)}_{p_0(\\cdot),q(\\cdot)}\\hookrightarrow B^{s_1(\\cdot)}_{p_1(\\cdot),p_0(\\cd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08985","kind":"arxiv","version":1},"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"}