Maximal estimates for orthonormal systems of wave equations with sharp regularity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918131275923456 |
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| author | Ko, Hyerim Lee, Sanghyuk Shiraki, Shobu |
| author_facet | Ko, Hyerim Lee, Sanghyuk Shiraki, Shobu |
| contents | We study maximal estimates for the wave equation with orthonormal initial data. In dimension $d=3$, we establish optimal results with the sharp regularity exponent up to the endpoint. In higher dimensions $d \ge 4$ and also in $d=2$, we obtain sharp bounds for the Schatten exponent (summability index) $β\in [2, \infty]$ when $d\ge4$, and $β\in[1, 2]$ when $d=2$, improving upon the previous estimates due to Kinoshita--Ko--Shiraki. Our approach is based on a novel analysis of a key integral arising in the case $β=2$, which allows us to refine existing techniques and achieve the optimal estimates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal estimates for orthonormal systems of wave equations with sharp regularity Ko, Hyerim Lee, Sanghyuk Shiraki, Shobu Analysis of PDEs Classical Analysis and ODEs We study maximal estimates for the wave equation with orthonormal initial data. In dimension $d=3$, we establish optimal results with the sharp regularity exponent up to the endpoint. In higher dimensions $d \ge 4$ and also in $d=2$, we obtain sharp bounds for the Schatten exponent (summability index) $β\in [2, \infty]$ when $d\ge4$, and $β\in[1, 2]$ when $d=2$, improving upon the previous estimates due to Kinoshita--Ko--Shiraki. Our approach is based on a novel analysis of a key integral arising in the case $β=2$, which allows us to refine existing techniques and achieve the optimal estimates. |
| title | Maximal estimates for orthonormal systems of wave equations with sharp regularity |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.19451 |