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A Note on Non-tangential Convergence for Schrödinger Operators
Journal of Fourier Analysis and Applications ( IF 1.2 ) Pub Date : 2021-06-16 , DOI: 10.1007/s00041-021-09862-x
Wenjuan Li , Huiju Wang , Dunyan Yan

The goal of this note is to establish non-tangential convergence results for Schrödinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the initial data which implies convergence. As a consequence, we obtain an upper bound for p such that the Schrödinger maximal function is bounded from \(H^{s}(\mathbb {R}^{n})\) to \(L^{p}(\mathbb {R}^{n})\) for any \(s > \frac{n}{2(n+1)}\).



中文翻译:

薛定谔算子非切向收敛的一个注记

本笔记的目的是为沿受限曲线的薛定谔算子建立非切向收敛结果。我们考虑这种逼近区域的维度与初始数据的规律性之间的关系,这意味着收敛。因此,我们获得了p的上限,使得薛定谔极大函数有界从\(H^{s}(\mathbb {R}^{n})\)\(L^{p}(\ mathbb {R}^{n})\)对于任何\(s > \frac{n}{2(n+1)}\)

更新日期:2021-06-17
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