• 论文 •

### QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

1. School of Applied Mathematics, Beijing Normal University, Zhuhai 519087, China
• 收稿日期:2018-03-18 出版日期:2019-08-25 发布日期:2019-09-12
• 通讯作者: Guoen HU E-mail:88558509@qq.com
• 作者简介:Wenhua GAO,E-mail:guoenxx@163.com
• 基金资助:
The research of the first author was supported by Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhai, and NNSF of China under Grant #11461065. The research of the second author was supported by the NNSF of China under grant #11871108.

### QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

Wenhua GAO, Guoen HU

1. School of Applied Mathematics, Beijing Normal University, Zhuhai 519087, China
• Received:2018-03-18 Online:2019-08-25 Published:2019-09-12
• Supported by:
The research of the first author was supported by Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhai, and NNSF of China under Grant #11461065. The research of the second author was supported by the NNSF of China under grant #11871108.

In this article, the authors consider the weighted bounds for the singular integral operator defined by

where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rn such that ▽A ∈ BMO(Rn). By sparse domination, the authors obtain some quantitative weighted bounds for TA when Ω satisfies regularity condition of Lr-Dini type for some r ∈ (1, ∞).

Abstract: In this article, the authors consider the weighted bounds for the singular integral operator defined by

where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rn such that ▽A ∈ BMO(Rn). By sparse domination, the authors obtain some quantitative weighted bounds for TA when Ω satisfies regularity condition of Lr-Dini type for some r ∈ (1, ∞).

• 42B20