{"paper":{"title":"$\\mathrm{L}^1$-estimates for constant rank operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bogdan Rai\\c{t}\\u{a}","submitted_at":"2018-11-25T17:07:37Z","abstract_excerpt":"We show that the inequality $$\n  \\|D^{k-1}(u-\\pi u)\\|_{\\mathrm{L}^{n/(n-1)}(\\mathbb{R}^n)}\\leq c\\|\\mathbb{B}(D) u\\|_{\\mathrm{L}^1(\\mathbb{R}^n)} $$ holds for vector fields $u\\in\\mathrm{C}^\\infty_c$ if and only if $\\mathbb{B}$ is canceling. Here $\\pi$ denotes the $\\mathrm{L}^2$-orthogonal projection onto the kernel of the $k$-homogeneous differential operator $\\mathbb{B}(D)$ of \\emph{constant rank} on $\\mathbb{R}^n$. Other critical embeddings are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10057","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"}