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.

引用

页码：521 / 536

页数：16

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