{"paper":{"title":"Gradient Estimate on the Neumann Semigroup and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Lixin Yan","submitted_at":"2010-09-10T09:41:29Z","abstract_excerpt":"We prove the following sharp upper bound for the gradient of the Neumann semigroup $P_t$ on a $d$-dimensional compact domain $\\OO$ with boundary either $C^2$-smooth or convex:\n  $$\\|\\nn P_t\\|_{1\\to \\infty}\\le \\ff{c}{t^{(d+1)/2}},\\ \\ t>0,$$ where $c>0$ is a constant depending on the domain and $\\|\\cdot\\|_{1\\to\\infty}$ is the operator norm from $L^1(\\OO)$ to $L^\\infty(\\OO)$. This estimate implies a Gaussian type point-wise upper bound for the gradient of the Neumann heat kernel, which is applied to the study of the Hardy spaces, Riesz transforms, and regularity of solutions to the inhomogeneous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1965","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"}