多线性分数次积分算子在Herz型Hardy空间中的有界性  

Boundedness of Multilinear Fractional Integral Operators on Herz Type Hardy Spaces

作　　者：张普能[1] 李亮[1] 

机构地区：[1]伊犁师范学院数学与统计学院应用数学研究所,新疆伊宁835000

出　　处：《四川师范大学学报（自然科学版）》2013年第5期721-725,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：新疆维吾尔自治区自然科学基金(2012211B28)资助项目

摘　　要：分数次积分算子是Riesz位势算子在高维空间中的推广,具有重要的应用背景,寻找具有合适光滑性条件的核函数使得多线性算子保持有界在算子领域的研究中具有重要地位.运用Sharp极大函数点态估计及Herz型Hardy空间的中心原子分解技术,证明了一类满足某种Hrmander条件的多线性分数次奇异积分算子是乘积Herz型Hardy空间到Herz空间有界的,该条件比经典条件具有更弱的光滑性,进而推广了经典分数次奇异积分算子的有界性结论.Fractional integral operator is the extension case of Riesz potential operator in higher dimension spaces which has important application background. The smooth condition of the kernel function which makes the muhilinear operator to preserve its boundedhess plays a key role in the research of the operator theory. Based on point-estimates of sharp maximal operator and the atom decomposition of the Herz type Hardy space, the authors established a class of multilinear fractional operators with kernel satisfying Hormander type condition which are bounded from Herz type Hardy spaces into Herz spaces. The result partially generalized the classical fractional operators＇ boundeness in a weak kernel sense.

关 键 词：多线性算子 分数次奇异积分 HERZ型HARDY空间 原子 

分 类 号：O177.6[理学—数学]