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arXiv · 2008.03093

A Note on Non-tangential Convergence for Schr\"{o}dinger Operators

Wenjuan Li·Huiju Wang·Dunyan Yan
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Abstract

The goal of this note is to establish non-tangential convergence results for Schr\"{o}dinger 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 a upper bound for $p$ such that the Schr\"{o}dinger maximal function is bounded from $H^{s}(\mathbb{R}^{n})$ to $L^{p}(\mathbb{R}^{n})$ for any $s > \frac{n}{2(n+1)}$.

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Wenjuan Li, Huiju Wang, Dunyan Yan. 2020-08-07. A Note on Non-tangential Convergence for Schr\"{o}dinger Operators. https://arxiv.org/abs/2008.03093

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