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Weak Orlicz spaces:Some basic properties and their applications to harmonic analysis 被引量:8

Weak Orlicz spaces:Some basic properties and their applications to harmonic analysis
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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. 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.
出处 《Science China Mathematics》 SCIE 2013年第4期789-802,共14页 中国科学:数学(英文版)
基金 supported by National Natural Science Foundation of China (Grant No.11071190)
关键词 weak Orlicz space NORMALITY maximal operator interpolation theorem singular integral operator Orlicz空间 调和分析 应用 特性 谐波分析 绝对连续性 插值定理 有界性
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