论文标题
缩放临界磁场的分数schrödinger方程的最大估计值
Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields
论文作者
论文摘要
在本文中，我们结合了[12]和[27]的论点，以证明分数schrödinger方程的最大估计值$（i \ partial_t+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \} _ {\ mathbf {a}}}^{a}}^{\fracα2}^{\fracα2}）u = 0 $ = 0 $ = 0 $，其中包括纯净磁性字段，其中包括Aharonov。该证明基于群集光谱量度估计。尤其是$α= 1 $，波动方程的最大估计值直到端点。
In this paper, we combine the argument of [12] and [27] to prove the maximal estimates for fractional Schrödinger equations $(i\partial_t+\mathcal{L}_{\mathbf{A}}^{\fracα2})u=0$ in the purely magnetic fields which includes the Aharonov-Bohm fields. The proof is based on the cluster spectral measure estimates. In particular $α=1$, the maximal estimate for wave equation is sharp up to the endpoint.
