Noncommutative analysis of Hermite expansions

2022/05/04 by Bang Xu, Xu, Bang
Mathematics · #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2205.02284

openalex publication_date 2022/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the study of Hermite operators acting on noncommutative L_p-spaces. In the first part, we establish the noncommutative maximal inequalities for Bochner-Riesz means associated with Hermite operators and then obtain the corresponding pointwise convergence theorems. In particular, we develop a noncommutative Stein\textquoteright s theorem of Bochner-Riesz means for the Hermite operators. The second part of this paper deals with two multiplier theorems for Hermite operators. Our analysis on this part is based on a noncommutative analogue of the classical Littlewood-Paley-Stein theory associated with Hermite expansions.

Related

• Bochner-Riesz means for the Hermite and special Hermite expansions
• The commutators of Bochner-Riesz Operators for Hermite operator
• Mixed norm estimates for Hermite multipliers
• Pointwise convergence of noncommutative Fourier series
• A weighted L² estimate of Commutators of Bochner-Riesz Operators for Hermite operator