TWO WEIGHT NORM INEQUALITIES FOR THE g FUNCTION

被引：18
|
作者：
Lacey, Michael T. [1 ]
Li, Kangwei [2 ,3 ]
机构：
[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
来源：
MATHEMATICAL RESEARCH LETTERS | 2014年 / 21卷 / 03期
基金：
澳大利亚研究理事会; 美国国家科学基金会;
关键词：
two weight inequalities; square functions; OPERATORS;
D O I：
10.4310/MRL.2014.v21.n3.a9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given two weights sigma, w on R-n, the classical g-function satisfies the norm inequality parallel to g(f sigma)parallel to(2)(L)(w) less than or similar to parallel to f parallel to (2)(L)(sigma) if and only if the two weight Muckenhoupt A(2) condition holds, and a family of testing conditions holds, namely integral integral(Q(I)) (del P-t(sigma 1(I))(x, t))(2) dw tdt less than or similar to sigma(I) uniformly over all cubes I subset of R-n, and Q(I) is the Carleson box over I. A corresponding characterization for the intrinsic square function of Wilson also holds.
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页码：521 / 536
页数：16
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