Weak-type endpoint bounds for Bochner–Riesz means for the Hermite operator

Abstract

We obtain weak-type $(p, p)$ endpoint bounds for Bochner–Riesz means for the Hermite operator $H = -\Delta + |x|^2$ in ${\mathbb{R}}^n, n\ge 2$ and for other related operators, for $1\le p\le 2n/(n+2)$, extending earlier results of Thangavelu and of Karadzhov.