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arXiv · 1508.05437

$L^p$-estimates of maximal function related to Schrödinger Equation in $\mathbb{R}^2$

Xiumin Du·Xiaochun Li
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Abstract

Using Guth's polynomial partitioning method, we obtain $L^p$ estimates for the maximal function associated to the solution of Schrödinger equation in $\mathbb R^2$. The $L^p$ estimates can be used to recover the previous best known result that $\lim_{t \to 0} e^{itΔ}f(x)=f(x)$ almost everywhere for all $f \in H^s (\mathbb{R}^2)$ provided that $s>3/8$.

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Xiumin Du, Xiaochun Li. 2016-11-09. $L^p$-estimates of maximal function related to Schrödinger Equation in $\mathbb{R}^2$. https://arxiv.org/abs/1508.05437

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