Abstract:We study the pointwise convergence of solutions to the free Schrödinger equation with initial data in the Bessel potential spaces $L_s^p(\mathbb{R}^n)$. We establish new sufficient regularity indices for pointwise convergence across the full range $1 \leq p < \infty$, and demonstrate via counterexamples that these indices are sharp for all $1 \leq p \leq 2$ in one dimension, as well as at the endpoint $p=1$ and $p>2+p_n$ in higher dimensions. The proofs rely on the high-dimensional stationary phase method.
| Comments: | 28 pages |
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 46E35, 42B37 |
| Cite as: | arXiv:2605.25833 [math.AP] |
| (or arXiv:2605.25833v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25833 arXiv-issued DOI via DataCite (pending registration) |
From: Wenchang Sun [view email]
[v1]
Mon, 25 May 2026 13:29:54 UTC (23 KB)
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