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arXiv · 2509.18003

The $L^p$-continuity of wave operators for fractional order Schr\"odinger operators

M. Burak Erdogan·Michael Goldberg·William Green
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Abstract

We consider fractional Schr\"odinger operators $H=(-\Delta)^\alpha+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2\alpha$, $\alpha>1$. We show that the wave operators extend to bounded operators on $L^p(\mathbb R^n)$ for all $1\leq p\leq\infty$ under conditions on the potential that depend on $n$ and $\alpha$ analogously to the case when $\alpha\in \mathbb N$. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schr\"odinger operator.

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M. Burak Erdogan, Michael Goldberg, William Green. 2025-09-22. The $L^p$-continuity of wave operators for fractional order Schr\"odinger operators. https://doi.org/10.1016/j.jfa.2026.111663

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