{"paper":{"title":"Weighted Caffarelli-Kohn-Nirenberg type inequalities related to Grushin type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Manli Song, Wenjuan Li","submitted_at":"2016-06-17T09:09:07Z","abstract_excerpt":"We consider the Grushin type operator on $\\mathbb{R}^{d}_x \\times \\mathbb{R}^{k}_y$ with the form \\begin{equation*} G_\\mu=\\overset{d}{\\underset{i=1}{\\sum}}\\partial_{x_i}^2+\\left(\\overset{d}{\\underset{i=1}{\\sum}}x_i^2\\right)^{2\\mu}\\overset{k}{\\underset{j=1}{\\sum}}\\partial_{y_j}^2. \\end{equation*} and derive weighted Hardy-Sobolev type inequalities and weighted Caffarelli-Kohn-Nirenberg type inequalities related to $G_\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06089","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"}