{"paper":{"title":"Riesz transforms on non-compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz, Jocelyn Magniez, Peng Chen","submitted_at":"2014-11-01T16:49:59Z","abstract_excerpt":"Let $M$ be a complete non-compact Riemannian manifold satisfying the doubling volume property\n  as well as a Gaussian upper bound for the corresponding heat kernel. We study the boundedness of the Riesz transform $d\\Delta ^{-\\frac{1}{2}}$ on both Hardy spaces $H^p$ and Lebesgue spaces $L^p$ under two different conditions on the negative part of the Ricci curvature $R^-$.\n  First we prove that if $R^-$ is $\\alpha$-subcritical for some $\\alpha \\in [0,1)$, then the Riesz transform $d^*\\Delta^{-\\frac{1}{2}}$ on differential $1$-forms is bounded from the associated Hardy space $H^p_{\\overrightarrow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0137","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"}