Sharp Endpoint Eigenfunction Estimates for the Two-Dimensional Hermite Operator

Guiyu Xie, Cheng Zhang

Let $\mathcal{H}=-\Delta +|x{|}^2$ be the Hermite operator on ${\mathbb{R}}^2$, and let ${\Pi }_{\lambda }$ denote the spectral projection corresponding to $\lambda =2N+2$. We prove the sharp log-free endpoint est…