A sharp Schrödinger maximal estimate in R[superscript 2]

Author(s)
Du, Xiumin; Li, Xiaochun; Guth, Lawrence
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Abstract
We show that lim[subscript t→0] e[superscript itΔ]f(x) = f(x) almost everywhere for all f ∈ H[superscript s](R[superscript 2]) provided that s > 1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.
Date issued
2017-08
URI
http://hdl.handle.net/1721.1/115564
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Annals of Mathematics
Publisher
Annals of Mathematics, Princeton U
Citation
Du, Xiumin, et al. “A Sharp Schrödinger Maximal Estimate in R[superscript 2].” Annals of Mathematics, vol. 186, no. 2, Sept. 2017, pp. 607–40.
Version: Author's final manuscript
ISSN
0003-486X
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