Boundary Strichartz estimates and pointwise convergence for orthonormal systems

TL;DR

This paper develops boundary Strichartz estimates and pointwise convergence results for orthonormal systems, extending previous work on fermionic systems and many-body estimates.

Contribution

It introduces new maximal estimates for fermionic systems, including boundary and maximal-in-time estimates, advancing understanding of pointwise convergence in this context.

Findings

Established boundary boundary Strichartz estimates for fermionic systems

Proved new maximal-in-time estimates for orthonormal systems

Extended previous results on Carleson's pointwise convergence problem

Abstract

We consider maximal estimates associated with fermionic systems. First we establish maximal estimates with respect to the spatial variable. These estimates are certain boundary cases of the many-body Strichartz estimates pioneered by Frank, Lewin, Lieb and Seiringer. We also prove new maximal-in-time estimates, thereby significantly extending work of Lee, Nakamura and the first author on Carleson's pointwise convergence problem for fermionic systems.