{"paper":{"title":"Fractional Hardy-Sobolev inequalities for canceling elliptic differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jorge Hounie, Tiago Picon","submitted_at":"2018-09-22T20:46:52Z","abstract_excerpt":"Let $A(D)$ be an elliptic homogeneous linear differential operator of order $\\nu$ on $\\mathbb{R}^{N}$, $N \\geq 2$, from a complex vector space E to a complex vector space F. In this paper we show that if $\\ell\\in \\mathbb{R}$ satisfies $0< \\ell <N$ and $\\ell \\leq \\nu$, then the estimate \\begin{equation}\\nonumber \\left(\\int_{\\mathbb{R}^{N}}| (-\\Delta)^{(\\nu-\\ell)/2}u(x)|^{q}|x|^{-N+(N-\\ell)q}\\,dx\\right)^{1/q}\\leq C \\|A(D)u\\|_{L^{1}} \\end{equation} holds for every $u \\in C_{c}^{\\infty}(\\mathbb{R}^{N};E)$ and $1\\le q<\\frac{N}{N-\\ell}$ if and only if $A(D)$ is canceling in the sense of V. Schafting"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08485","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"}