Weighted norm estimates of noncommutative Calderón-Zygmund operators

2025/01/09 by Wenfei Fan, Fan, Wenfei, Yong Jiao +5 · 1 citation
Mathematics · #46L52 (Primary) 42B20 (Secondary) #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2501.04951

openalex publication_date 2025/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type (1,1) estimate of noncommutative maximal Calderón-Zygmund operators, corresponding version of square functions and a weighted H₁- L₁ type inequality. All these results are obtained under the condition that the weight belonging to the Muchenhoupt A₁ class and certain regularity assumptions imposed on kernels which are weaker than the Lipschitz condition.

Cited by

• Maximal inequalities for square functions associated to group metric measure spaces

Related

• Maximal singular integral operators acting on noncommutative L_p-spaces
• Weighted Endpoint Estimates for Commutators of Calderón-Zygmund Operators
• Noncommutative maximal strong L_p estimates of Calderón-Zygmund operators
• Noncommutative weak type (1,1) estimates for Calderón-Zygmund operators with a class of L₁-integral conditions
• Weighted mixed endpoint estimates of Fefferman-Stein type for commutators of singular integral operators