Weighted inequalities for multilinear fractional integral operators

被引：128
|
作者：
Moen, Kabe [1 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
来源：
COLLECTANEA MATHEMATICA | 2009年 / 60卷 / 02期
基金：
美国国家科学基金会;
关键词：
Fractional integrals; maximal operators; weighted norm inequalities; multilinear operators; NORM INEQUALITIES; SINGULAR-INTEGRALS; MAXIMAL OPERATORS;
D O I：
10.1007/BF03191210
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A weighted theory for multilinear fractional integral operators and maximal functions is presented. Sufficient conditions for the two weight inequalities of these operators are found, including "power and logarithmic bumps" and an A(infinity) condition. For one weight inequalities a necessary and sufficient condition is then obtained as a consequence of the two weight inequalities. As an application, Poincare and Sobolev inequalities adapted to the multilinear setting are presented.
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页码：213 / 238
页数：26
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