Fractional integral operators on anisotropic hardy spaces

被引：7

作者：

Ding, Yong ^{[1
]}

Lan, Senhua ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Sch Mat Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

[2] Lishui Univ, Dept Math, Zhejiang 323000, Peoples R China

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2008年 / 60卷 / 03期

关键词：

anisotropic Hardy space; weak anisotropic Hardy space; fractional integral; multilinear operator; commutator;

D O I：

10.1007/s00020-008-1561-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce the fractional integral operator T of degree a of order m with respect to a dilation A for 0 < alpha < 1 and m is an element of N. First we establish the Hardy-Littlewood-Sobolev inequalities for T on anisotropic Hardy spaces associated with dilation A, which show that T is bounded from H-p to H-q, or from H-p to L-q, where 0 < p <= 1/(1 + alpha) and 1/q = 1/p - alpha. Then we give anisotropic Hardy spaces estimates for a class of multilinear operators formed by fractional integrals or Calder'on-Zygmund singular integrals. Finally, we apply the above results to give the boundedness of the commutators of T and a BMO function.

引用

页码：329 / 356

页数：28

共 23 条

[1] Boundedness of operators on Hardy spaces via atomic decompositions [J].