{"paper":{"title":"Mapping properties of the Schr\\\"odinger maximal function on Damek--Ricci spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Swagato K. Ray, Utsav Dewan","submitted_at":"2024-11-06T18:06:03Z","abstract_excerpt":"For $f \\in \\mathscr{S}^2(\\mathcal S)_{o}$, the collection of radial $L^2$-Schwartz class functions on Damek--Ricci spaces $\\mathcal S$, we consider the Schr\\\"odinger maximal function, \\begin{equation*} S^* f(x):= \\displaystyle\\sup_{0<t<4/Q^2} \\left|S_tf(x)\\right|\\:,\\:\\:\\:\\:\\:\\:x\\in\\mathcal S\\:, \\end{equation*} corresponding to the Laplace--Beltrami operator $\\Delta$ with initial data $f$. We first obtain the complete description of the pairs $(q, \\alpha) \\in [1, \\infty] \\times [0,\\infty)$ for which the estimate \\begin{equation*} {\\|S^*f\\|}_{L^q\\left(B_R\\right)} \\le C_R\\: {\\|f\\|}_{H^{\\alpha}(\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04084","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.04084/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"}