Orthonormal Strichartz estimates for Dunkl-Schrödinger equation of initial data with Sobolev regularity

Abstract: Let $\Delta_\kappa$ be the Dunkl-Laplacian on $\mathbb{R}^n$. The main aim of this paper is to investigate the orthonormal Strichartz estimates for the Schr\"odinger equation with initial data from the homogeneous Dunkl-Sobolev space $\dot{H}\kappa^s (\mathbb{R}^n)$. Our approach is based on restricted weak-type orthonormal estimates, frequency-localized estimates for the Dunkl-Schr\"odinger propagator $e^{it\Delta\kappa}$, and a series of successive real and complex interpolation techniques.