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

• 论文 • 上一篇    下一篇

MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

何少勇1, 陈杰诚2   

  1. 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. 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: 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