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<p>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.</p>

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Maximal estimates for orthonormal systems of wave equations

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Shinya Kinoshita,
  • Hyerim Ko,
  • Shobu Shiraki

摘要

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.