截口上的奇异积分高阶交换子的加权估计

刘爽

(西北师范大学数学与信息科学学院,甘肃 兰州 730070)

截口上的奇异积分高阶交换子的加权估计

刘爽

(西北师范大学数学与信息科学学院,甘肃 兰州 730070)

研究截口上的奇异积分高阶交换子f(x),利用截口F关于核的ki(x,y)估计,在一定假设下得到了的Sharp极大函数估计和加权弱(1,1)型估计.

关奇异积分;高阶交换子;截口;BMOF

1 引言及主要定理

2 预备知识与记号

3 定理的证明

[1]Aimar H,Forzani L,Toledano R.Ball and quasi-metrics:A space of homogeneous type modeling the real analysis related to the Monge-Amp`ere equation[J].J.Fourier Anal.Appl.,1998,4(2):377-381.

[2]Ca ff arelli L A,Gutierez C E.Real analysis related to the Monge-Amp`ere equation[J].Trans.Amer.Math. Soc.,1996,348(3):1075-1092.

[3]Ca ff arelli L A,Gutierez C E.Singular integrals related to the Monge-Amp`ere equation[J].Appl.Numer. Harmon.Anal.,1997(1):3-13.

[4]Incognito A.Weak-type(1,1)inequality for the Monge-Amp`ere equation[J].J.Fourier.Anal.Appl., 2001,7(1):41-48. [5]Tang L.Weighted estimates for singular integral operators and commutators associated with the sections[J]. J.Math.Anal.Appl.,2007,333(3):577-590.

[6]P´erez C.Endpoint estimates for commutators of singular integral operators[J].J.Funct.Anal.,1995, 128(1):163-185.

[7]P´erez C,Gonz´alez R.Sharp weighted estimates for vector-valued singular integral operators and commutators[J].Tohoku.Math.J.,2003,55(1):109-129.

[8]Rao M M,Ren Z D.Theory of Orlicz Spaces[M].New York:Marcel Dekker,1991.

[9]陶双平,牛耀明.粗糙核奇异积分交换子在 Triebel-Lizorkin的有界性 [J].纯粹数学与应用数学,2010,26(1): 29-35.

Weighted estimated for higher order commutators of singular integral operators associated with the sections

Liu Shuang
(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China)

The aim of this paper is to study the weighted estimates for the higher order commutators of singular integral operatorsf(x).Under some hypotheses of ki(x,y)associated with the sections F,the sharp maximal functions and the weighted weak-type(1,1)estimates foris obtained.

singular integral operators,higher order commutators,sections,BMOF

O174.2

A

1008-5513(2012)01-0058-09

2012-10-18.

国家自然科学基金(11161042;11071250).

刘爽(1970-),硕士,讲师,研究方向：调和分析.

2010 MSC:42B20,42B25,42B35