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arXiv · 2608.21823

Endpoint orthonormal Strichartz estimates

Sonae Hadama·Shunya Toyoshima
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Abstract

We establish the orthonormal Strichartz estimates in the abstract Keel--Tao framework, under precisely the same hypotheses as in their original theorem. As an important consequence, we resolve the endpoint conjecture for the Schr\"odinger equation in dimensions $d\ge 2$, which was first raised by Frank, Lewin, Lieb, and Seiringer. This consequence also yields an affirmative answer to the conjecture for the free transport equation, which was stated in dual form by Bennett, Bez, Guti\'errez, and Lee. As a further application, we also establish a refinement of the Strichartz estimate for a single function.

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Sonae Hadama, Shunya Toyoshima. 2026-08-22. Endpoint orthonormal Strichartz estimates. https://arxiv.org/abs/2608.21823

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