[1]陈冬香,毛素珍.带非光滑核的多线性奇异积分极大算子的有界性[J].江西师范大学学报(自然科学版),2012,(04):343-346.
　CHEN Dong-xiang,MAO Su-zhen.The Boundedness of the Maximal Multilinear Singular Integral Operator with Non-Smooth Kernel[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(04):343-346.
点击复制

带非光滑核的多线性奇异积分极大算子的有界性()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年04期
页码:
343-346
栏目:
出版日期:
2012-08-01

文章信息/Info

Title:
The Boundedness of the Maximal Multilinear Singular Integral Operator with Non-Smooth Kernel
作者:
陈冬香;毛素珍
江西师范大学数学与信息科学学院 江西 南昌 330022
Author(s):
CHEN Dong-xiang;  MAO Su-zhen
关键词:
多线性奇异积分算子; 非光滑核; 恒等逼近; Cotlar不等式; 极大算子
Keywords:
multilinear singular integral operator;  non-smooth kernel;  approximation to the identity;  Cotlar inequality;  maximal operator
分类号:
O626.4
文献标志码:
A
摘要:
利用极大算子的 sharp 极大函数的点态估计方法,建立了具有非光滑核的多线性奇异积分极大算子的Cotlar型不等式,应用Cotlar不等式证明了极大算子是Lr(Rn)到Lp0(Rn)上的有界算子,推广了一些已知结果.
Abstract:
Using the pointwise estimates of sharp maximal function for the maximal singular integrals, the cotlar inequality for the maximal multilinear singular integral operator with non-smooth kernels is established and it is proved that the maximal operator is bounded from Lr(Rn) into Lp0(Rn). Some known results are extended.

参考文献/References:

[1] Calderon A P, Zygmund A. On commutators of singular integrals [J]. Studia Math, 1975, 53(2): 139-174.
[2] Duong X T, McIntosh A. Singular integral operators with non-smooth kernels on irregular domains [J]. Rev Mat Iberoa-mericana, 1999, 15(2): 233-265.
[3] Deng Donggao, Yan Lixin. Commutators of singular integral operators with non-smooth kernels [J]. Acta Math Sci, 2005, 25(1): 137-144.
[4] Cohen J, Gosssenlin J. On multilinear singular integrals [J]. Studia Math, 1986, 30(3): 445-464.
[5] Hu Yue. On mutiliear fractional integrals [J]. Approx Theory Appl, 1985, l(3): 33-51.
[6] Calderon A P. Commutators of singular integral operators [J]. Proc Nat Acad Sci USA, 1965, 53(5): 1092-1099.
[7] 曾志强, 陈冬香. 具有H(m)一型核的奇异积分算子交换子的双权Lipschitz估计 [J]. 江西师范大学学报: 自然科学版, 2011, 35(6): 601-604.
[8] Crafakos L, Torres R H. Multilinear Calderon-Zygmund theory [J]. Advances in Math, 2002, 165(1): 124-164.
[9] 李倩丽, 毛素珍, 陈冬香. 强奇异Calderon-Zygmund算子的交换子的双权BMO估计 [J]. 数学研究, 2012, 45(1): 45-53.
[10] 曹小牛, 陈冬香. 广义分数积分多线性交换子的端点估计 [J]. 江西师范大学学报: 自然科学版, 2010, 34(2): 205-207.
[11] Hu Guoen, Yang Dachun. Maximal commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of homogeneous type [J]. Math Anal Appl, 2009, 354(1): 249-262.
[12] Hu Guoen. Lp boundedness for the multilinear singlar integral operator [J]. Integr Equ Oper Theory, 2005, 52(3): 437-449.

更新日期/Last Update: 1900-01-01