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

TL;DR

This paper establishes weak-type endpoint bounds for Bochner-Riesz means associated with the Hermite operator in multiple dimensions, extending previous results and broadening the understanding of these bounds in harmonic analysis.

Contribution

It provides new weak-type endpoint bounds for Bochner-Riesz means for the Hermite operator, extending earlier work by Thangavelu and Karadzhov.

Findings

Established weak-type (p,p) bounds for 1 ≤ p ≤ 2n/(n+2)

Extended previous results to higher dimensions and broader operator classes

Enhanced understanding of harmonic analysis related to 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 ${\mathbb R}^n, n\geq 2$ and for other related operators for $1\leq p\leq 2n/(n+2)$, extending earlier results of Thangavelu and of Karadzhov.