Strichartz estimates involving orthonormal systems at the critical summability exponent
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909696975175680 |
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| author | Feng, Guoxia Song, Manli Wu, Huoxiong |
| author_facet | Feng, Guoxia Song, Manli Wu, Huoxiong |
| contents | The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schrödinger operator $e^{itΔ}$ with initial data from the homogeneous Sobolev space $\dot{H}^s (\mathbb{R}^n)$. We prove new global strong-type orthonormal Strichartz estimates in the interior of $ODCA$ at the optimal summability exponent $α=q$, thereby substantially supplymenting the work of Bez-Hong-Lee-Nakamura-Sawano \cite{Bez-Hong-Lee-Nakamura-Sawano}. Our approach is based on restricted weak-type orthonormal estimates, real interpolation argument and the advantageous condition $q<p$ in the interior of $ODCA$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_14974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates involving orthonormal systems at the critical summability exponent Feng, Guoxia Song, Manli Wu, Huoxiong Analysis of PDEs 35Q41, 42B37, 35B65 The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schrödinger operator $e^{itΔ}$ with initial data from the homogeneous Sobolev space $\dot{H}^s (\mathbb{R}^n)$. We prove new global strong-type orthonormal Strichartz estimates in the interior of $ODCA$ at the optimal summability exponent $α=q$, thereby substantially supplymenting the work of Bez-Hong-Lee-Nakamura-Sawano \cite{Bez-Hong-Lee-Nakamura-Sawano}. Our approach is based on restricted weak-type orthonormal estimates, real interpolation argument and the advantageous condition $q<p$ in the interior of $ODCA$. |
| title | Strichartz estimates involving orthonormal systems at the critical summability exponent |
| topic | Analysis of PDEs 35Q41, 42B37, 35B65 |
| url | https://arxiv.org/abs/2507.14974 |