QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

doi:10.1007/s10473-019-0417-x

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 1149-1162.doi: 10.1007/s10473-019-0417-x

QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

高文华, 胡国恩

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

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.

摘要/Abstract

摘要：

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 T_A when Ω satisfies regularity condition of L^r-Dini type for some r ∈ (1, ∞).

关键词: Singular integral operator, sparse domination, A_p constant, maximal operator

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 T_A when Ω satisfies regularity condition of L^r-Dini type for some r ∈ (1, ∞).

Key words: Singular integral operator, sparse domination, A_p constant, maximal operator

中图分类号:

42B20

高文华, 胡国恩. QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS[J]. 数学物理学报(英文版), 2019, 39(4): 1149-1162.

Wenhua GAO, Guoen HU. QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS[J]. Acta mathematica scientia,Series B, 2019, 39(4): 1149-1162.

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QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

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