Weak Type Estimates for Square Functions of Dunkl Heat Flows

2021/01/07 by Huaiqian Li, Li, Huaiqian
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2101.04056

openalex publication_date 2021/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The weak (1,1) boundedness of the Littlewood--Paley--Stein square function for the Dunkl heat flow is proved via estimates on the Dunkl heat kernel of integral type and the Caldrón--Zygmund decomposition, which is the continuity of the recently work [arXiv:2003.11843] where the dimension-free L^p boundedness of the same square function is studied.

Citations

• Differential-difference operators associated to reflection groups
• On the Generalized Ornstein-Uhlenbeck Semigroup

Related

• Littlewood--Paley--Stein inequalities on \textupRCD(K,∞) spaces
• Square function and heat flow estimates on domains
• Upper and lower bounds for Littlewood-Paley square functions in the Dunkl setting
• Littlewood-Paley-Stein operators on Damek-Ricci spaces
• Upper and lower bounds for Dunkl heat kernel