Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves

Eunhee Jeong; Hyerim Ko

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arXiv · 2610.23576

Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves

Eunhee Jeong·Hyerim Ko

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Abstract

We establish orthonormal maximal estimates for one-dimensional fractional Schrödinger operators along curves that are Hölder continuous in time and bi-Lipschitz in space. For both the convex range $m>1$ and the concave range $0<m<1$, we obtain sharp Sobolev regularity in terms of the order $m$. As an application, we obtain almost everywhere convergence of the associated densities to their initial values along the curves. The proof combines Schatten duality with kernel estimates.

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BibTeX RIS

Eunhee Jeong, Hyerim Ko. 2026-10-16. Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves. https://arxiv.org/abs/2610.23576

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