Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves

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.