On quantitative weighted bounds for commutators of rough singular integral operators
Abstract
Let $ \Omega $ be a homogeneous function of degree zero, integrable, and have a mean value of zero on the unit sphere $ \mathbb S^{n-1} $, $ n \geq 2 $. Let $ T_\Omega $ be the homogeneous convolution singular integral operator with kernel $ \frac{\Omega(x)}{|x|^n} $. In this paper, we proved some quantitative two-weight estimates for the commutator, $ [b, T_\Omega] $, with a $ BMO $ symbol $ b $ and the singular integral operator $ T_\Omega $ under the condition $ \Omega\in L^q(\mathbb{S}^{n-1}) $ for $ q\in (2, \infty) $.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Holomorphic and Operator Theory
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 1
- Pages
- 2111–2130
- Publication date
- 1 January 2026