极大变指标Herz空间上的参数型粗糙核Littlewood-Paley算子  

Parameterized Littlewood-Paley operators with rough kernel on grand variable Herz spaces

作　　者：史鹏伟 陶双平 SHI Peng-wei;TAO Shuang-ping(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2022年第12期45-54,共10页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金项目(12161080)。

摘　　要：借助变指标Lebesgue空间上的有界性,利用函数分层分解和实变技巧,得到了参数型粗糙核Marcinkiewicz积分、面积积分和Littlewood-Paley g^(*)_(λ)函数在极大变指标Herz空间上的有界性。同时也证明了面积积分和Littlewood-Paley g^(*)_(λ)函数高阶交换子的有界性。With the help of the boundedness of the Lebesgue space with variable exponent, by applying hierarchical decomposition of function and real variable techniques, the boundedness of the parameterized Marcinkiewicz integral, the area integral and Littlewood-Paley g^(*)_(λ)function with rough kernel is obtained on grand variable Herz spaces. Meanwhile, the boundedness of higher order commutators generated by the area integral and Littlewood-Paley g^(*)_(λ)function is also proved on grand variable Herz spaces.

关 键 词：极大变指标Herz空间 粗糙核 参数型Littlewood-Paley算子 高阶交换子 

分 类 号：O174.2[理学—数学]