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arXiv · 2605.25833

Pointwise Convergence of Schr\"{o}dinger Operators in Bessel Potential Spaces

Yucheng Pan·Wenchang Sun·Jiheng Tan
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Abstract

We study the pointwise convergence of solutions to the free Schr\"{o}dinger 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.

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Yucheng Pan, Wenchang Sun, Jiheng Tan. 2026-05-25. Pointwise Convergence of Schr\"{o}dinger Operators in Bessel Potential Spaces. https://arxiv.org/abs/2605.25833

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