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

作　　者：Takeshi Kawazoe 

机构地区：[1]Department of Mathematics, Keio University at SFC, Endo, Fujisawa, Kanagawa,252-8520, Japan

出　　处：《Analysis in Theory and Applications》2016年第1期38-51,共14页分析理论与应用（英文刊）

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

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.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.

关 键 词：Jacobi analysis Jacobi hypergroup g function area function real Hardy space. 

分 类 号：O212[理学—概率论与数理统计]