MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

doi:10.1007/s10473-022-0217-6

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 690-714.doi: 10.1007/s10473-022-0217-6

MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

何少勇¹, 陈杰诚²

1. Department of Mathematics, Huzhou University, Huzhou 313000, China;
2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2020-01-22 修回日期:2020-09-09 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Shaoyong HE,E-mail:hsyongmath@zjnu.edu.cn E-mail:hsyongmath@zjnu.edu.cn
作者简介:Jiecheng CHEN,E-mail:jcchen@zjnu.edu.cn
基金资助:
Supported by Zhejiang Provincial Natural Science Foundation of China (LQ22A010018) and National Natural Science Foundation of China (12071437).

MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

Shaoyong HE¹, Jiecheng CHEN²

1. Department of Mathematics, Huzhou University, Huzhou 313000, China;
2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received:2020-01-22 Revised:2020-09-09 Online:2022-04-25 Published:2022-04-22
Supported by:
Supported by Zhejiang Provincial Natural Science Foundation of China (LQ22A010018) and National Natural Science Foundation of China (12071437).

摘要/Abstract

摘要： The purpose of this paper is to introduce bi-parameter mixed Lipschitz spaces and characterize them via the Littlewood-Paley theory. As an application, we derive a boundedness criterion for singular integral operators in a mixed Journé class on mixed Lipschitz spaces. Key elements of the paper are the development of the Littlewood-Paley theory for a special mixed Besov spaces, and a density argument for the mixed Lipschitz spaces in the weak sense.

关键词: Mixed Lipschitz spaces, Littlewood-Paley theory, singular integral operators

Abstract: The purpose of this paper is to introduce bi-parameter mixed Lipschitz spaces and characterize them via the Littlewood-Paley theory. As an application, we derive a boundedness criterion for singular integral operators in a mixed Journé class on mixed Lipschitz spaces. Key elements of the paper are the development of the Littlewood-Paley theory for a special mixed Besov spaces, and a density argument for the mixed Lipschitz spaces in the weak sense.

Key words: Mixed Lipschitz spaces, Littlewood-Paley theory, singular integral operators

中图分类号:

42B35

何少勇, 陈杰诚. MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS[J]. 数学物理学报(英文版), 2022, 42(2): 690-714.

Shaoyong HE, Jiecheng CHEN. MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS[J]. Acta mathematica scientia,Series B, 2022, 42(2): 690-714.

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MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

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