NECESSARY CONDITIONS FOR THE BOUNDEDNESS OF LINEAR AND BILINEAR COMMUTATORS ON BANACH FUNCTION SPACES

被引：14
|
作者：
Chaffee, Lucas [1 ]
Cruz-Uribe, David [2 ]
机构：
[1] Western Washington Univ, Dept Math, Bellingham, WA 98225 USA
[2] Univ Alabama, Dept Math, Box 870350, Tuscaloosa, AL 35487 USA
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2018年 / 21卷 / 01期
基金：
美国国家科学基金会;
关键词：
BMO; commutators; singular integrals; fractional integrals; bilinear operators; weights; variable Lebesgue spaces; WEIGHTED NORM INEQUALITIES; MEAN-OSCILLATION; OPERATORS; EXTRAPOLATION;
D O I：
10.7153/mia-2018-21-01
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we extend recent results by the first author [3] on the necessity of BMO for the boundedness of commutators on the classical Lebesgue spaces. We generalize these results to a large class of Banach function spaces. We show that with modest assumptions on the underlying spaces and on the operator T, if the commutator [b, T] is bounded, then the function b is in BMO.
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页码：1 / 16
页数：16
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