BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE∗

doi:10.1007/s10473-023-0409-8

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1587-1602.doi: 10.1007/s10473-023-0409-8

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE^∗

Xiangxing TAO¹, Yuan ZENG^1,†, Xiao YU²

1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China;
2. Department of Mathematics, Shangrao Normal University, Shangrao 334001, China

收稿日期:2022-01-24 发布日期:2023-08-08
通讯作者: †Xiangxing TAO, E-mail: zy1347256531@163.com
作者简介:Xiangxing TAO, E-mail: xxtau@163.com; Xiao YU, E-mail: yx2000s@163.com
基金资助:
*This research was supported by the NNSF of China (12271483, 11961056) and the NSF of Jiangxi Province (20192BAB201004). Zeng's research supported by the “Xin-Miao” Program of Zhejiang Province (2021R415027) and the Innovation Fund of ZUST (2020yjskc06).

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE^∗

Xiangxing TAO¹, Yuan ZENG^1,†, Xiao YU²

1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China;
2. Department of Mathematics, Shangrao Normal University, Shangrao 334001, China

Received:2022-01-24 Published:2023-08-08
Contact: †Xiangxing TAO, E-mail: zy1347256531@163.com
About author:Xiangxing TAO, E-mail: xxtau@163.com; Xiao YU, E-mail: yx2000s@163.com
Supported by:
*This research was supported by the NNSF of China (12271483, 11961056) and the NSF of Jiangxi Province (20192BAB201004). Zeng's research supported by the “Xin-Miao” Program of Zhejiang Province (2021R415027) and the Innovation Fund of ZUST (2020yjskc06).

摘要/Abstract

摘要： In this paper, the authors consider the $\omega$-type Calderón-Zygmund operator $T_{\omega}$ and the commutator $[b,T_{\omega}]$ generated by a symbol function $b$ on the Lorentz space $L^{p,r}(X)$ over the homogeneous space $(X,d,\mu)$. The boundedness and the compactness of the commutator $[b,T_{\omega}]$ on Lorentz space $L^{p,r}(X)$ are founded for any $p\in (1, \infty)$ and $r\in [1, \infty)$.

关键词: $\omega$-type Calderón-Zygmund operator, commutators, Lorentz space, homogeneous space

Abstract: In this paper, the authors consider the $\omega$-type Calderón-Zygmund operator $T_{\omega}$ and the commutator $[b,T_{\omega}]$ generated by a symbol function $b$ on the Lorentz space $L^{p,r}(X)$ over the homogeneous space $(X,d,\mu)$. The boundedness and the compactness of the commutator $[b,T_{\omega}]$ on Lorentz space $L^{p,r}(X)$ are founded for any $p\in (1, \infty)$ and $r\in [1, \infty)$.

Key words: $\omega$-type Calderón-Zygmund operator, commutators, Lorentz space, homogeneous space

Xiangxing TAO, Yuan ZENG, Xiao YU. BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1587-1602.

Xiangxing TAO, Yuan ZENG, Xiao YU. BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1587-1602.

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BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE^∗

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERÓN-ZYGMUND OPERATOR ON LORENTZ SPACE^∗

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