Weak Orlicz spaces: Some basic properties and their applications to harmonic analysis

被引：22
|
作者：
Liu PeiDe [1 ]
Wang MaoFa [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 04期
基金：
中国国家自然科学基金;
关键词：
weak Orlicz space; normality; maximal operator; interpolation theorem; singular integral operator; LORENTZ SPACES;
D O I：
10.1007/s11425-012-4452-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis. We first discuss the absolute continuity of the quasi-norm and its normality, then prove the boundedness of several maximal operators. We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces. As applications, the weak type analogues of several classical inequalities in harmonic analysis is obtained.
引用
收藏
页码：789 / 802
页数：14
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