{"paper":{"title":"Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David S. McCormick, James C. Robinson, Jose L. Rodrigo","submitted_at":"2013-03-26T00:07:22Z","abstract_excerpt":"Using elementary arguments based on the Fourier transform we prove that for $1 \\leq q < p < \\infty$ and $s \\geq 0$ with $s > n(1/2-1/p)$, if $f \\in L^{q,\\infty}(\\R^n) \\cap \\dot{H}^s(\\R^n)$ then $f \\in L^p(\\R^n)$ and there exists a constant $c_{p,q,s}$ such that\n  \\[ \\|f\\|_{L^p} \\leq c_{p,q,s} \\|f\\|_{L^{q,\\infty}}^\\theta \\|f\\|_{\\dot H^s}^{1-\\theta}, \\] where $1/p = \\theta/q + (1-\\theta)(1/2-s/n)$. In particular, in $\\R^2$ we obtain the generalised Ladyzhenskaya inequality $\\|f\\|_{L^4}\\le c\\|f\\|_{L^{2,\\infty}}^{1/2}\\|f\\|_{\\dot H^1}^{1/2}$. We also show that for $s=n/2$ the norm in $\\|f\\|_{\\dot H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6351","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"}