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arXiv · 2508.19446

Maximal estimates for orthonormal systems of wave equations

Shinya Kinoshita·Hyerim Ko·Shobu Shiraki
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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.

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Shinya Kinoshita, Hyerim Ko, Shobu Shiraki. 2025-08-26. Maximal estimates for orthonormal systems of wave equations. https://arxiv.org/abs/2508.19446

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