Yinghao Gong | Searcharxiv

arXiv2026

Critical orthonormal Strichartz estimates for Lebesgue spaces

We study orthonormal Strichartz estimates at the critical coefficient exponent $q/2$ for fractional Schrödinger propagators. The proof for $d\geq3$ combines annular Schatten estimates with a frequency summation argument based on potential duality and Littlewood--Paley theory. In dimension two, a trace computation supplies the annular estimate needed for the global estimate. We also construct a counterexample to the global estimate with spatial $L^\infty$ and coefficients in $\ell^{q/2}$, even with a weak time norm.

math.AP↗

arXiv2026

Critical Strichartz estimates for orthonormal systems

Orthonormal Strichartz estimates for the free Schrödinger propagator take the form \begin{equation*} \left\Vert\sum_jλ_j\left|e^{itΔ}f_j\right|^2\right\Vert_{L_t^\frac{q}{2}L_x^\frac{r}{2}(\mathbb{R}\times\mathbb{R}^d)}\lesssim\Vertλ\Vert_{\ell^α(\mathbb{C})} \end{equation*}for arbitrary orthonormal systems $(f_j)_j$ in the homogeneous Sobolev space $\dot{H}^s(\mathbb{R}^d)$. In the admissible region, the optimal range of $α$ has been established when $q\geq r/d'$. For $d\geq2$ 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 $r<\infty$. Our approach is robust and we illustrate this by extending the result to fractional Schrödinger propagators.

math.AP↗