Restricted Testing for Positive Operators

被引：1

作者：

Hytonen, Tuomas ^{[1
]}

Li, Kangwei ^{[2
,3
]}

Sawyer, Eric ^{[4
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, Pietari Kalmin Katu 5,POB 68, Helsinki 00014, Finland

[2] Tianjin Univ, Ctr Appl Math, Weijin Rd 92, Tianjin 300072, Peoples R China

[3] Basque Ctr Appl Math, BCAM, Mazarredo 14, Bilbao Basque Country 48009, Spain

[4] McMaster Univ, Dept Math & Stat, 1280 Main St West, Hamilton, ON L8S 4K1, Canada

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 11期

基金：

芬兰科学院;

关键词：

Two weight T(1) theorems; Positive operators; Restricted testing conditions; REAL VARIABLE CHARACTERIZATION; WEIGHT NORM INEQUALITIES; 2-WEIGHT INEQUALITY; HILBERT TRANSFORM; THEOREM;

D O I：

10.1007/s12220-021-00675-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for certain positive operators T, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant D > 1, depending only on the dimension n, such that the two weight norm inequality integral(Rn) T (f sigma)(2) d omega <= C integral(Rn) f(2)d sigma holds for all f >= 0 if and only if the (fractional) A(2) condition holds, and the restricted testing condition integral(Q) T (1 Q(sigma))(2) d omega <= C vertical bar Q vertical bar(sigma) holds for all cubes Q satisfying vertical bar 2Q|(sigma) = D vertical bar Q vertical bar(sigma). If T is linear, we require as well that the dual restricted testing condition integral(Q) T* (1(Q)holds for all cubes Q satisfying vertical bar 2Q vertical bar(omega) <= D vertical bar Q vertical bar(omega).omega)(2) d sigma <= C vertical bar Q vertical bar(omega).

引用

页码：11139 / 11164

页数：26

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