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

Abstract

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

30 pages