NEW WEIGHTED ESTIMATES FOR BILINEAR FRACTIONAL INTEGRAL OPERATORS

被引：1

作者：

Moen, Kabe ^{[1
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 02期

基金：

美国国家科学基金会;

关键词：

Bilinear operators; fractional integration; weighted inequalities; NORM INEQUALITIES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a plethora of weighted estimates for bilinear fractional integral operators of the form BI alpha(f, g)(x) = integral(Rn) f(x - t)g(x + t)/vertical bar t vertical bar(n - alpha) dt, 0 < alpha < n. When the target space has an exponent greater than one, many weighted estimates follow trivially from Holder's inequality and the known linear theory. We address the case where the target Lebesgue space is at most one and prove several interesting one and two weight estimates. As an application we formulate a bilinear version of the Stein-Weiss inequality for fractional integrals.

引用

页码：627 / 646

页数：20

共 22 条

[1]

Cruz-Uribe D. V., ILLINOIS J IN PRESS

[2] SHARP NORM INEQUALITIES FOR COMMUTATORS OF CLASSICAL OPERATORS [J].