{"paper":{"title":"Improved Poincare inequalities with weights","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Irene Drelichman, Ricardo G. Dur\\'an","submitted_at":"2007-11-21T15:48:24Z","abstract_excerpt":"In this paper we prove that if $\\Omega\\in\\mathbb{R}^n$ is a bounded John domain, the following weighted Poincare-type inequality holds: $$ \\inf_{a\\in \\mathbb{R}}\\| (f(x)-a) w_1(x) \\|_{L^q(\\Omega)} \\le C \\|\\nabla f(x) d(x)^\\alpha w_2(x) \\|_{L^p(\\Omega)} $$ where $f$ is a locally Lipschitz function on $\\Omega$, $d(x)$ denotes the distance of $x$ to the boundary of $\\Omega$, the weights $w_1, w_2$ satisfy certain cube conditions, and $\\alpha \\in [0,1]$ depends on $p,q$ and $n$. This result generalizes previously known weighted inequalities, which can also be obtained with our approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3399","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"}