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数学进展 - 2018, Vol. 47(1): 81-94
研究论文
非齐性测度空间上的Marcinkiewicz积分的交换子的端点估计
Endpoint Estimates for Commutators of the Marcinkiewicz Integrals over Non-homogeneous Metric Measure Spaces

房成龙, 曹勇辉, 周疆
FANG Chenglong, CAO Yonghui*, ZHOU Jiang

新疆大学数学与系统科学学院, 乌鲁木齐, 新疆, 830046
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 81-94
DOI: 10.11845/sxjz.2016062b


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摘要 令$(\mathcal{X},d,\mu)$是 Hytönen给出的满足几何双倍与上有界双倍的度量测度空间. 本文主要目的是去证明Marcinkiewicz积分的交换子从$L\log L(\mu)$到$L^{1,\infty}(\mu)$及$H^{1,\infty}_{\rm a t b}(\mu)$到$L^{1,\infty}(\mu)$的有界性.
关键词 非齐性测度空间Marcinkiewicz积分交换子RBMO$(\mu)$Hardy空间    
Abstract:Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions in the sense of Hyt\"{o}nen. The aim of this paper is to establish the boundedness of the commutators of the Marcinkiewicz integrals, from $L\log L(\mu)$ to $L^{1,\infty}(\mu)$ and from $H^{1,\infty}_{\rm atb}(\mu)$ to $L^{1,\infty}(\mu)$ respectively.
Key wordsnon-homogeneous metric measure spaces    Marcinkiewicz integrals    commutator    RBMO$(\mu)$    Hardy space
PACS:  O174.2  
通讯作者: E-mail: $*$ 445476616@qq.com   
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