分数次极大算子及其交换算子在Lie群作用下的广义Orlicz-Morrey空间上的估计
Fractional Maximal Operator and Its Commutator on Generalized Orlicz-Morrey Spaces over Lie Groups
DOI: 10.12677/PM.2022.129157, PDF, HTML, 下载: 305  浏览: 2,051  科研立项经费支持
作者: 芮俪, 逯光辉*, 李雪梅：西北师范大学数学与统计学院，甘肃 兰州
关键词: 分数次极大算子；交换子；广义Orlicz-Morrey空间；BMO(G)空间；Lie群；Fractional Maximal Operator； Commutator； Generalized Orlicz-Morrey Space； Space BMO(G)； Lie Group
摘要: 本文首先给出分层李群G作用下的广义Orlicz-Morrey空间MΦ,φ(G)的定义，其次利用HO¨lder不等式以及函数分界方法，得到了分数次极大算子Mα在此空间上的有界性估计，最后证明了分数次极大算子Mα与BMO及其与BMO函数生成的交换子Mb,α从MΦ,φ(G)到Mψ,η(G)上的有界性。
Abstract: This article first gives the definition of generalized Orlicz-Morrey MΦ,φ(G) on stratified Lie group G; second proves that the fractional maximal operator Mα is bounded from spaces MΦ,φ(G) into spaces Mψ,η(G) by means of HO¨lder inequality and the method of function decomposition. Furthermore, the boundedness of the commutator Mb,α generated by b∈BMO(G) from spaces MΦ,φ(G) into spaces Mψ,η(G) is also obtained.
文章引用：芮俪, 逯光辉, 李雪梅. 分数次极大算子及其交换算子在Lie群作用下的广义Orlicz-Morrey空间上的估计[J]. 理论数学, 2022, 12(9): 1441-1456. https://doi.org/10.12677/PM.2022.129157

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