{"paper":{"title":"Weighted Hardy's inequalities and Kolmogorov-type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelaziz Rhandi, Anna Canale, Cristian Tacelli, Federica Gregorio","submitted_at":"2017-03-30T17:04:43Z","abstract_excerpt":"We give general conditions to state the weighted Hardy inequality \\[ c\\int_{\\mathbb{R}^N}\\frac{\\varphi^2} {|x|^2}d\\mu\\leq\\int_{\\mathbb{R}^N}|\\nabla \\varphi |^2 d\\mu+C\\int_{\\mathbb{R}^N} \\varphi^2d\\mu,\\quad \\varphi\\in C_c^{\\infty}(\\mathbb{R}^N),\\,c\\leq c_{0,\\mu}, \\] with respect to a probability measure $d\\mu$. Moreover, the optimality of the constant $c_{0,\\mu}$ is given. The inequality is related to the following Kolmogorov equation perturbed by a singular potential \\[ Lu+Vu=\\left(\\Delta u+\\frac{\\nabla \\mu}{\\mu}\\cdot \\nabla u\\right)+\\frac{c}{|x|^2}u \\] for which the existence of positive solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10567","kind":"arxiv","version":2},"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"}