H^1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis Ⅱ

作     者：Takeshi Kawazoe 

作者机构：Department of Mathematics Keio University at SFC Endo Fujisawa Kanagawa252-8520 Japan 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2016年第32卷第1期

页      面：38-51页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：partly supported by Grant-in-Aid for Scientific Research (C) No.24540191  Japan Society for the Promotion of Science 

主　　题：Jacobi analysis Jacobi hypergroup g function area function real Hardy space. 

摘      要：Abstract. Let （R＋,＊,A） be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley g function and the Lusin area function for the Jacobi hypergroup and consider their （H^1, L^1 ） boundedness. Although the g operator for （R＋,＊,A） possesses better property than the classical g operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the （H^1,L^1） estimate for the Lusin area operator, a slight modification in its form is required.