{"paper":{"title":"Maximal estimates for fractional Schr\\\"odinger equations in scaling critical magnetic fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haoran Wang, Jiye Yuan","submitted_at":"2022-01-05T13:33:26Z","abstract_excerpt":"In this paper, we combine the argument of [12] and [27] to prove the maximal estimates for fractional Schr\\\"odinger equations $(i\\partial_t+\\mathcal{L}_{\\mathbf{A}}^{\\frac\\alpha 2})u=0$ in the purely magnetic fields which includes the Aharonov-Bohm fields. The proof is based on the cluster spectral measure estimates. In particular $\\alpha=1$, the maximal estimate for wave equation is sharp up to the endpoint."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.01600","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/2201.01600/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"}