{"paper":{"title":"Functional Inequalities for Convolution Probability Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Jian Wang","submitted_at":"2013-08-07T23:33:59Z","abstract_excerpt":"Let $\\mu$ and $\\nu$ be two probability measures on $\\R^d$, where $\\mu(\\d x)= \\e^{-V(x)}\\d x$ for some $V\\in C^1(\\R^d)$. Explicit sufficient conditions on $V$ and $\\nu$ are presented such that $\\mu*\\nu$ satisfies the log-Sobolev, Poincar\\'e and super Poincar\\'e inequalities. In particular, the recent results on the log-Sobolev inequality derived in \\cite{Z} for convolutions of the Gaussian measure and compactly supported probability measures are improved and extended."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1713","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"}