{"paper":{"title":"$L^p$-estimates of maximal function related to Schr\\\"{o}dinger Equation in $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xiaochun Li, Xiumin Du","submitted_at":"2015-08-21T23:56:16Z","abstract_excerpt":"Using Guth's polynomial partitioning method, we obtain $L^p$ estimates for the maximal function associated to the solution of Schr\\\"odinger equation in $\\mathbb R^2$. The $L^p$ estimates can be used to recover the previous best known result that $\\lim_{t \\to 0} e^{it\\Delta}f(x)=f(x)$ almost everywhere for all $f \\in H^s (\\mathbb{R}^2)$ provided that $s>3/8$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05437","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"}