{"paper":{"title":"Sharp $L^p$ estimates for Schr\\\"odinger groups on spaces of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Fabio Nicola, Piero D'Ancona, The Anh Bui","submitted_at":"2016-12-05T08:01:18Z","abstract_excerpt":"We prove an $L^{p}$ estimate $$ \\|e^{-itL} \\varphi(L)f\\|_{p}\\lesssim (1+|t|)^s\\|f\\|_p, \\qquad t\\in \\mathbb{R}, \\qquad s=n\\left|\\frac{1}{2}-\\frac{1}{p}\\right| $$ for the Schr\\\"odinger group generated by a semibounded, selfadjoint operator $L$ on a metric measure space $\\mathcal{X}$ of homogeneous type (where $n$ is the doubling dimension of $\\mathcal{X}$). The assumptions on $L$ are a mild $L^{p_{0}}\\to L^{p_{0}'}$ smoothing estimate and a mild $L^{2}\\to L^{2}$ off--diagonal estimate for the corresponding heat kernel $e^{-tL}$. The estimate is uniform for $ \\varphi$ varying in bounded sets of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01267","kind":"arxiv","version":3},"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"}