On quantitative weighted bounds for commutators of rough singular integral operators

Peize Lv; Xiangxing Tao; Peize Lv; Xiangxing Tao

doi:10.3934/math.2026087

AIMS Mathematics

2026, Volume 11, Issue 1: 2111-2130. doi: 10.3934/math.2026087

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Research article

On quantitative weighted bounds for commutators of rough singular integral operators

Peize Lv ^,,
Xiangxing Tao

Department of Mathematics, School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, China

Received: 09 September 2025 Revised: 13 January 2026 Accepted: 16 January 2026 Published: 22 January 2026
MSC : 42B20

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) $.
- quantitative weighted estimate,
- commutator,
- singular integral,
- rough kernel of $ L^q $ type
Citation: Peize Lv, Xiangxing Tao. On quantitative weighted bounds for commutators of rough singular integral operators[J]. AIMS Mathematics, 2026, 11(1): 2111-2130. doi: 10.3934/math.2026087

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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) $.

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