劉爽

(西北師范大學數(shù)學與信息科學學院,甘肅 蘭州 730070)

截口上的奇異積分高階交換子的加權估計

劉爽

(西北師范大學數(shù)學與信息科學學院,甘肅 蘭州 730070)

研究截口上的奇異積分高階交換子f(x),利用截口F關于核的ki(x,y)估計,在一定假設下得到了的Sharp極大函數(shù)估計和加權弱(1,1)型估計.

關奇異積分;高階交換子;截口;BMOF

1 引言及主要定理

2 預備知識與記號

3 定理的證明

[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]陶雙平,牛耀明.粗糙核奇異積分交換子在 Triebel-Lizorkin的有界性 [J].純粹數(shù)學與應用數(shù)學,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.

國家自然科學基金(11161042;11071250).

劉爽(1970-),碩士,講師,研究方向：調(diào)和分析.

2010 MSC:42B20,42B25,42B35