Multi-parameter Triebel-Lizorkin and Besov Spaces Associated with Flag Singular Integrals  

作　　者：Yong DING Guo Zhen LU Bo Lin MA 

机构地区：[1]Laboratory of Mathematics and Complex Systems ( BNU), Ministry of Education, P. R. China [2]School of Mathematics, Beijing Normal University, Beijing 100875, P. R. China [3]Department of Mathematics, Wayne State University, Detroit 48202, USA [4]College of Mathematics and Information Engineering, Jiaxing University, Jiaxing 314001, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第4期603-620,共18页数学学报（英文版）

基　　金：supported partly by NSF of China (No. 10571015);SRFDP of China (No. 20050027025);supported by the U.S. NSF (Grant DMS No. 0500853);supported partly by NSF of China (No. 10771054);supported by NSF of China (No, 10811120558)

摘　　要：Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.

关 键 词：flag singular integrals multiparameter Triebel-Lizorkin spaces discrete Calderdn repro- ducing formulas discrete Littlewood-Paley-Stein analysis 

分 类 号：O174.41[理学—数学] O177.6[理学—基础数学]