On the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators

TL;DR

This paper establishes the optimal Schatten exponent condition for orthonormal Strichartz estimates related to Dunkl operators, extending known results for classical Laplacian and Hermite cases.

Contribution

It provides a necessary condition on the Schatten exponent for these estimates, demonstrating its optimality in the context of Dunkl operators.

Findings

Identifies the optimal Schatten exponent condition.

Extends results to Dunkl Laplacian and Dunkl-Hermite operators.

Provides a necessary condition that matches known cases.

Abstract

In \cite{PRA} and \cite{SSM} the orthonormal Strichartz estimates for the Schr\"odinger equation associated with the Dunkl Laplacian and the Dunkl-Hermite operator are obtained. In this article, we prove a necessary condition on the Schatten exponent for the above orthonormal Strichartz estimates, which turns out to be optimal for the Schr\"odinger equations associated with Laplacian and Hermite operator as a special case.