PreprintarXiv licencearXiv
Critical Strichartz estimates for orthonormal systems
Abstract
Orthonormal Strichartz estimates for the free Schrödinger propagator take the form ‖∑jλj|eitΔfj|2‖Lt/q2Lx/r2(ℝ×ℝd)≲‖λ‖ℓα(ℂ)for arbitrary orthonormal systems (fj)j in the homogeneous Sobolev space Ḣs(ℝd). In the admissible region, the optimal range of α has been established when q≥ r/d'. For d≥2 and 2<q<r/d', it has been an open question as to determine whether the estimate holds when α=q/2. We prove that the estimate holds in this critical case whenever q=4 and r<∞. Our approach is robust and we illustrate this by extending the result to fractional Schrödinger propagators.
Related
- Critical orthonormal Strichartz estimates for Lebesgue spaces
- Orthonormal Strichartz estimates over fractal time
- Orthonormal Strichartz estimates for the Schrödinger equations with Hamiltonian on Wiener amalgam spaces
- Maximal estimates of the Schrödinger operators with quadratic potential for orthonormal systems
- Sharp critical Strichartz estimates for a resonant hyperbolic Schrödinger flow on the 3D waveguide
BibTeX
@misc{gong2026critical,
title = {{Critical Strichartz estimates for orthonormal systems}},
author = {Yinghao Gong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.22805},
eprint = {2608.22805},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22805},
}
RIS
TY - UNPB
TI - Critical Strichartz estimates for orthonormal systems
AU - Yinghao Gong
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2608.22805
UR - https://arxiv.org/abs/2608.22805
AB - Orthonormal Strichartz estimates for the free Schrödinger propagator take the form ‖∑_jλ_j|e^itΔf_j|^2‖_L_t^/q2L_x^/r2(ℝ×ℝ^d)≲‖λ‖_ℓ^α(ℂ)for arbitrary orthonormal systems (f_j)_j in the homogeneous Sobolev space Ḣ^s(ℝ^d). In the admissible region, the optimal range of α has been established when q≥ r/d'. For d≥2 and 2<q<r/d', it has been an open question as to determine whether the estimate holds when α=q/2. We prove that the estimate holds in this critical case whenever q=4 and r<∞. Our approach is robust and we illustrate this by extending the result to fractional Schrödinger propagators.
ER -