Schr dinger解的点态收敛性和多线性精化Schr hartz估计
Pointwise convergence of Schrödinger solutions and multilinear refined Strichartz estimates
摘要：
在分形测度的一般情况下，我们对薛定谔解的点态收敛问题得到了部分改进。特别地，我们证明了，对于$n\geq 3$，$\lim_{t \to 0} e^{itΔ}f(x) = f(x)$几乎处处相对于勒贝格测度所有$f \in H^s (\mathbb{R}^n)$提供的$s>(n+1)/2(n+2)$。证明使用线性精化的Escherichartz估计。我们还证明了一个多线性细化的Eschhartz使用解耦和多线性Kakeya。
英文摘要：
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 $n\geq 3$, $\lim_{t \to 0} e^{itΔ}f(x) = f(x)$ 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.
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