Strichartz estimates involving orthonormal systems at the critical summability exponent

Abstract: The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the Schr\"odinger operator $e^{it\Delta}$ 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 $\alpha=q$, 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 $ODCA$.