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 for $p=1$ or $p$ large enough in higher dimensions. The proofs rely on the high-dimensional stationary phase method.
From: Wenchang Sun [view email]
[v1]
Mon, 25 May 2026 13:29:54 UTC (23 KB)
[v2]
Tue, 26 May 2026 14:37:17 UTC (23 KB)
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