Maximal estimates for orthonormal systems of wave equations

TL;DR

This paper advances the understanding of maximal estimates for wave operators applied to orthonormal systems, using geometric analysis and Schatten estimates to improve results in low-dimensional cases.

Contribution

It introduces a novel geometric approach leveraging Schatten $2$ estimates and Wolff's lemma to extend maximal estimates for orthonormal systems of wave equations.

Findings

Extended maximal estimates for orthonormal systems in low dimensions.

Applied geometric analysis of wave operator kernels.

Utilized Schatten $2$ estimates and Wolff's geometric lemma.

Abstract

This paper investigates maximal estimates of the wave operators for orthonormal families of initial data. We extend the classical maximal estimates for the wave operator by making partial progress on maximal estimates for orthonormal systems in low dimensions. Our novel approach is based on a geometric analysis of the kernel of wave operators within the framework of Schatten $2$ estimates. In particular, we exploit Wolff's geometric lemma on the intersection patterns of thickened spheres.