Orthonormal Strichartz estimates for Dunkl-Schr\"{o}dinger equation of initial data with Sobolev regularity

TL;DR

This paper establishes orthonormal Strichartz estimates for the Dunkl-Schrödinger equation with initial data in Dunkl-Sobolev spaces, extending harmonic analysis tools to Dunkl operators.

Contribution

It introduces restricted weak-type orthonormal estimates and frequency-localized bounds for the Dunkl-Schrödinger propagator, advancing analysis in Dunkl harmonic analysis.

Findings

Proved orthonormal Strichartz estimates for Dunkl-Schrödinger equation.

Developed frequency-localized estimates for the Dunkl-Schrödinger propagator.

Applied interpolation techniques to derive main results.

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.