A sharp Schrödinger maximal estimate in R[superscript 2]
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1612.08946.pdf
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372.54 KB
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Author(s)
Du, Xiumin
Li, Xiaochun
Guth, Lawrence
Date Issued
August 2017
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4007/ANNALS.2017.186.2.5
