Sharp weighted bounds for fractional integral operators

被引：92

作者：

Lacey, Michael T. ^{[2
]}

Moen, Kabe ^{[3
]}

Perez, Carlos ^{[1
]}

Torres, Rodolfo H. ^{[3
]}

机构：

[1] Univ Seville, Dept Anal Matemat, Fac Matemat, E-41080 Seville, Spain

[2] Georgia Inst Technol, Dept Math, Atlanta, GA 30332 USA

[3] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 05期

基金：

美国国家科学基金会;

关键词：

Maximal operators; Fractional integrals; Singular integrals; Weighted norm inequalities; Extrapolation; Sharp bounds; NORM INEQUALITIES; EXTRAPOLATION; SPACES;

D O I：

10.1016/j.jfa.2010.02.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds arc obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities arc obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities. (C) 2010 Published by Elsevier Inc.

引用

页码：1073 / 1097

页数：25

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