Maximal estimates for orthonormal systems of wave equations

Shinya Kinoshita; Hyerim Ko; Shobu Shiraki

doi:10.1007/s11854-025-0431-y

Maximal estimates for orthonormal systems of wave equations

Shinya Kinoshita
, Hyerim Ko
, Shobu Shiraki^*

^*Corresponding author for this work

Department of Mathematics

Institute of Science Tokyo
University of Lisbon

Research output: Contribution to journal › Journal article › peer-review

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.

Original language	English
Pages (from-to)	683-713
Number of pages	31
Journal	Journal d'Analyse Mathematique
Volume	158
Issue number	2
DOIs	https://doi.org/10.1007/s11854-025-0431-y
State	Published - 2026.05

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10.1007/s11854-025-0431-y

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title = "Maximal estimates for orthonormal systems of wave equations",

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{\textquoteright}s geometric lemma on the intersection patterns of thickened spheres.",

author = "Shinya Kinoshita and Hyerim Ko and Shobu Shiraki",

note = "Publisher Copyright: {\textcopyright} The Hebrew University of Jerusalem 2025.",

year = "2026",

month = may,

doi = "10.1007/s11854-025-0431-y",

language = "English",

volume = "158",

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AU - Kinoshita, Shinya

AU - Ko, Hyerim

AU - Shiraki, Shobu

N1 - Publisher Copyright: © The Hebrew University of Jerusalem 2025.

PY - 2026/5

Y1 - 2026/5

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/105025165714

U2 - 10.1007/s11854-025-0431-y

DO - 10.1007/s11854-025-0431-y

M3 - Journal article

AN - SCOPUS:105025165714

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VL - 158

SP - 683

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JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

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Maximal estimates for orthonormal systems of wave equations

Abstract

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New Mathematics Study Findings Have Been Reported by Investigators at Department of Mathematics (Maximal Estimates for Orthonormal Systems of Wave Equations)

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Maximal estimates for orthonormal systems of wave equations

Abstract

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New Mathematics Study Findings Have Been Reported by Investigators at Department of Mathematics (Maximal Estimates for Orthonormal Systems of Wave Equations)

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