Work

A noncommutative weak $L_1$-estimate for rough singular integrals

Year: 2026

Type: preprint

Abstract: In this paper, we establish a noncommutative version of Andreas Seeger's weak type $(1,1)$ estimate for singular integral operators with kernels satisfying angular $L\log L$ integrability and an averaged radial Dini condition. The strategy for obtaining the sharp integrability condition involves not only some new estimates of the off-diagonal good and bad functions in Parcet's noncommutative Calderón-Zygmund decomposition but also certain essential modifications of Seeger's kernel decomposition and estimates.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.25339

Authors: Hong, Guixiang, Wang, Liang, Wang, Xumin, Xu, Bang

Institutions: Harbin Institute of Technology, Xiamen University, City University of Hong Kong

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: City University of Hong Kong, National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Award: G5343799843

OpenAlex ID: W7223050939

Cites: 1

Cited by:

Related to: 10