Noncommutative weak type (1,1) estimates for Calderón-Zygmund operators with a class of L₁-integral conditions

2025/12/07 by Lai, Xudong, Xu, Lingxin
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Approximation Theory and Sequence Spaces

paper · doi:10.48550/arxiv.2512.06843

Abstract

We construct a slightly new noncommutative Calderón-Zygmund decomposition by further splitting the bad function. Using this tool, we prove the weak type (1,1) boundedness of noncommutative Calderón-Zygmund operators under a class of L₁-integral conditions, which are close to L₁-Dini conditions.

Citations

• Spectral multipliers in group algebras and noncommutative Calderón-Zygmund theory
• Maximal singular integral operators acting on noncommutative L_p-spaces
• Noncommutative maximal operators with rough kernels
• Weak boundedness of Calderón-Zygmund operators on noncommutative L₁-spaces
• Noncommutative Riesz transforms -- Dimension free bounds and Fourier multipliers
• Smooth Fourier multipliers on group von Neumann algebras
• Pseudo-localization of singular integrals and noncommutative Littlewood-Paley inequalities
• Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory
• Doob's inequality for non-commutative martingales
• Estimates for translation invariant operators in Lp spaces
• On the existence of certain singular integrals

Related

• Weak boundedness of Calderón-Zygmund operators on noncommutative L₁-spaces
• Noncommutative maximal strong L_p estimates of Calderón-Zygmund operators
• Weighted norm estimates of noncommutative Calderón-Zygmund operators
• Noncommutative maximal operators with rough kernels
• Noncommutative weak (1,1) type estimate for a square function from ergodic theory