加权Hardy算子交换子在Herz型空间中的中心BMO估计
Central BMO Estimates for Commutators of Weighted Hardy Operators on Herz Type Spaces
DOI: 10.12677/PM.2013.33025, PDF, HTML, 下载: 3,129  浏览: 6,971  国家科技经费支持
作者: 龚淑丽*：湖南大学数学与计量经济学院；侯宪明：临沂大学数学系
关键词: 加权Hardy算子；交换子；中心BMO空间；Herz型空间； Weighted Hardy Operator; Commutator; Central BMO Space; Herz Type Space
摘要: 给出了一个关于权函数满足的充分条件，该条件使得加权Hardy算子与中心BMO函数生成的交换子在Herz型空间中有界。进一步地，将所得结论推广到了k阶的情形。
Abstract: In this paper, we present sufficient conditions on weighted function which ensures the boundedness of commutators generated by weighted Hardy operators and central BMO functions on Herz spaces and Morrey-Herz spaces, respectively. Moreover, the corresponding results are extended to the case of k-th order.
文章引用：龚淑丽, 侯宪明. 加权Hardy算子交换子在Herz型空间中的中心BMO估计[J]. 理论数学, 2013, 3(3): 169-175. http://dx.doi.org/10.12677/PM.2013.33025

参考文献

[1] C. Carton-Lebrun, M. Fosset. Moyennes et quotients de Taylor dans BMO. Bulletin de la Société Royale des Sciences de Liège, 1984, 53(2): 85-87.
[2] Z. W. Fu, L. Grafakos, S. Z. Lu and F. Y. Zhao. Sharp bounds for m-linear Hardy operators and Hilbert operators. Houston Journal of Mathematics, 2012, 38(1): 225-244.
[3] F. Y. Zhao, Z. W. Fu and S. Z. Lu. Endpoint estimates for n-dimensional Hardy operators and their commutators. Science China Mathematics, 2012, 55(10): 1977-1990.
[4] J. Xiao. Lp and bounds of weighted Hardy-Littlewood averages. Journal of Mathematical Analysis and Applications, 2001, 262(2): 660-666.
[5] R. Fefferman. Characterization of bounded mean oscillation. Bulletin of the American Mathematical Society, 1971, 77: 587-588.
[6] Z. W. Fu, Z. G. Liu and S. Z. Lu. Commutators of weighted Hardy operators on Rn. Proceedings of the American Mathematical Society, 2009, 137(10): 3319-3328.
[7] Z. W. Fu, S. Z. Lu and W. Yuan. A weighted variant of Riemann-Liouville fractional integral on Rn. Abstract and Applied Analysis, 2012, 2012: 18 p.
[8] S. Z. Lu, D. C. Yang. The central BMO spaces and Littlewood-Paley operators. Approximation Theory and its Applications, 1995, 11(3): 72- 94.
[9] S. Z. Lu, D. C. Yang. The decomposition of the weighted Herz spaces on Rn and its application. Science in China Series A: Mathematics, 1995, 38(2): 147-158.
[10] S. Z. Lu, L. F. Xu. Boundedness of rough singular integral operators on the homogenous Morrey-Herz spaces. Hokkaido Mathematical Journal, 2005, 34(2): 299-314.
[11] 刘宗光, 傅尊伟. Herz空间中的加权Hardy-Littlewood平均算子[J]. 数学学报, 2006, 49(5): 1085-1090.
[12] Z. W. Fu, S. Z. Lu. A remark on weighted Hardy-Littlewood averages on Herz spaces. Advances in Mathematics (China), 2008, 37(5): 632- 636.

为你推荐