Maximal estimates for orthonormal systems of wave equations

Hyerim Ko; Shinya Kinoshita; Shobu Shiraki

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arxiv 2508.19446 v1 pith:S2MSH2ID submitted 2025-08-26 math.AP math.CA

Maximal estimates for orthonormal systems of wave equations

Shinya Kinoshita , Hyerim Ko , Shobu Shiraki This is my paper

classification math.AP math.CA

keywords estimatesmaximalwaveorthonormalgeometricoperatorssystemsanalysis

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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.

Maximal estimates for orthonormal systems of wave equations

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