%A Shaoyong HE, Jiecheng CHEN %T MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS %0 Journal Article %D 2022 %J Acta mathematica scientia,Series B %R 10.1007/s10473-022-0217-6 %P 690-714 %V 42 %N 2 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16678.shtml} %8 2022-04-25 %X 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.