{"paper":{"title":"Convergence problem of Schr\\\"odinger equation in Fourier-Lebesgue spaces with rough data and random data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Yan, Xiangqian Yan, Yajuan Zhao","submitted_at":"2020-11-06T01:29:12Z","abstract_excerpt":"In this paper, we consider the convergence problem of Schr\\\"odinger equation. Firstly, we show the almost everywhere pointwise convergence of Schr\\\"odinger equation in Fourier-Lebesgue spaces $\\hat{H}^{\\frac{1}{p},\\frac{p}{2}}(\\mathbb{R})(4\\leq p<\\infty),$ $\\hat{H}^{\\frac{3 s_{1}}{p},\\frac{2p}{3}}(\\mathbb{R}^2)(s_{1}>\\frac{1}{3},3\\leq p<\\infty),$ $\\hat{H}^{\\frac{2 s_{1}}{p},p}(\\mathbb{R}^n)(s_{1}>\\frac{n}{2(n+1)},2\\leq p<\\infty,n\\geq3)$ with rough data. Secondly, we show that the maximal function estimate related to one Schr\\\"odinger equation can fail with data in $\\hat{H}^{s,\\frac{p}{2}}(\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.07134","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/2011.07134/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"}