THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS

doi:10.1007/s10473-020-104-1

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 45-58.doi: 10.1007/s10473-020-104-1

THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS

李金霞¹, 李宝德², 何建勋¹

1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China;
2. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

收稿日期:2019-02-25 修回日期:2019-05-16 出版日期:2020-02-25 发布日期:2020-04-14
通讯作者: Jianxun He E-mail:hejianxun@gzhu.edu.cn
基金资助:
The first author was supported by the “Basic Innovation” Program of Graduate Students of Guangzhou University (2018GDJC-D01); the second author is supported by the National Natural Science Foundation of China (11861062, 11661075 and 11561065) and the third author is supported by the the National Natural Science Foundation of China (11671414).

THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS

Jinxia LI¹, Baode LI², Jianxun HE¹

1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China;
2. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Received:2019-02-25 Revised:2019-05-16 Online:2020-02-25 Published:2020-04-14
Contact: Jianxun He E-mail:hejianxun@gzhu.edu.cn
Supported by:
The first author was supported by the “Basic Innovation” Program of Graduate Students of Guangzhou University (2018GDJC-D01); the second author is supported by the National Natural Science Foundation of China (11861062, 11661075 and 11561065) and the third author is supported by the the National Natural Science Foundation of China (11671414).

摘要/Abstract

摘要： Let T be an anisotropic Calderón-Zygmund operator and φ : Rⁿ×[0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function with φ(x, ·) being an Orlicz function and φ(·, t) being a Muckenhoupt A_∞(A) weight. In this paper, our goal is to study two boundedness theorems for commutators of anisotropic Calderón-Zygmund operators. Precisely, when b ∈ BMO_w(Rⁿ, A) (a proper subspace of anisotropic bounded mean oscillation space BMO(Rⁿ, A)), the commutator [b, T] is bounded from anisotropic weighted Hardy space H_w¹(Rⁿ, A) to weighted Lebesgue space L_w¹(Rⁿ) and when b ∈ BMO(Rⁿ) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space L^φ(Rⁿ), which are extensions of the isotropic setting.

关键词: expansive dilation, Muckenhoupt weight, weighted Hardy space, Calderón-Zygmund operator, commutator

Abstract: Let T be an anisotropic Calderón-Zygmund operator and φ : Rⁿ×[0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function with φ(x, ·) being an Orlicz function and φ(·, t) being a Muckenhoupt A_∞(A) weight. In this paper, our goal is to study two boundedness theorems for commutators of anisotropic Calderón-Zygmund operators. Precisely, when b ∈ BMO_w(Rⁿ, A) (a proper subspace of anisotropic bounded mean oscillation space BMO(Rⁿ, A)), the commutator [b, T] is bounded from anisotropic weighted Hardy space H_w¹(Rⁿ, A) to weighted Lebesgue space L_w¹(Rⁿ) and when b ∈ BMO(Rⁿ) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space L^φ(Rⁿ), which are extensions of the isotropic setting.

Key words: expansive dilation, Muckenhoupt weight, weighted Hardy space, Calderón-Zygmund operator, commutator

中图分类号:

42B35

李金霞, 李宝德, 何建勋. THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS[J]. 数学物理学报(英文版), 2020, 40(1): 45-58.

Jinxia LI, Baode LI, Jianxun HE. THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS[J]. Acta mathematica scientia,Series B, 2020, 40(1): 45-58.

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THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS

THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERÓN-ZYGMUND OPERATORS

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