Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 690-714.doi: 10.1007/s10473-022-0217-6

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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).

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

CLC Number: 

  • 42B35