一类算子在Triebel-Lizorkin空间的有界性  

A Class of Operator Bounded on Triebel-Lizorkin Spaces

作　　者：李晓冬[1] 牛耀明[1] 

机构地区：[1]包头师范学院数学科学学院,内蒙古包头014030

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2013年第1期5-7,共3页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10761005;11161042;11261035);内蒙古自治区高等学校科学研究项目(NJZZ12198)

摘　　要：利用Littlewood-Paley分解及权估计,在Triebel-Lizorkin空间上得到了一类奇异积分算子在Tf（x）=＋∞∑j=-∞ Kj＊f（x））的有界性.作为应用,对粗糙核奇异积分算子TΩf（x）=p.v.∫R″（Ω（y）/ρ（y）^β）f（x-y）dy,也得到了相应的结果,从而推广了已有结果.It is well-known that the Triebel-Lizorkin space F·α,qp（Rn） is a unified setting of many well-known function spaces including Lebesgue spaces Lp（Rn）,the Hardy spaces Hp（Rn） and the Sobolev spaces Lαp（Rn）.So it is very meaningful to study the boundedness on Triebel-Lizorkin spaces for sigular integral operators.For a class of sigular integral operators defined by Tf（x）=＋∞∑j=-∞ Kj＊f（x）,the boundedness on Triebel-Lizorkin spaces are obtained by using the Littlewood-Paley decomposition and the estimates of weight.As a application,for the rough kernel singular integral defined by TΩf（x）=p.v.∫R″（Ω（y）/ρ（y）^β）f（x-y）dydy.the corresponding result is also obtained.Therefore,the known result are extended.

关 键 词：粗糙核 奇异积分算子 TRIEBEL-LIZORKIN空间 

分 类 号：O177.2[理学—数学]