{"paper":{"title":"Riesz transform and $L^p$ cohomology for manifolds with Euclidean ends","license":"","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Gilles Carron (LMJL), Thierry Coulhon","submitted_at":"2004-11-30T09:28:53Z","abstract_excerpt":"Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\\RR^n \\setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz transform on $M$ is bounded from $L^p(M) \\to L^p(M; T^*M)$ for $1 < p < n$ and unbounded for $p \\geq n$ if there is more than one end. It follows from known results that in such a case the Riesz transform on $M$ is bounded for $1 < p \\leq 2$ and unbounded for $p > n$; the result is new for $2 < p \\leq n$. We also give some heat kernel estimates on such manifolds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411648","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0411648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}