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POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES

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sword-2019-11-13T16:38:13.original.xml (130 B)
Original SWORD entry document
Author(s)
DU, XIUMIN
•
GUTH, LARRY
•
LI, XIAOCHUN
•
ZHANG, RUIXIANG
Date Issued
2018
Journal
Forum of Mathematics, Sigma
Publisher
Cambridge University Press (CUP)
Version
Final published version
Abstract
We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geqslant 3$, $\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$$=f(x)$ almost everywhere with respect to Lebesgue measure for all $f\in H^{s}(\mathbb{R}^{n})$ provided that $s>(n+1)/2(n+2)$. The proof uses linear refined Strichartz estimates. We also prove a multilinear refined Strichartz using decoupling and multilinear Kakeya.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1017/FMS.2018.11
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