ε算子族与H^p空间的刻画

The e family of operators and characterizations of Hardy spaces H^p(R^n)

首先研究了用ε算子族定义的广义Lusin面积函数在L^P(R^n)(1<p<∞)上的有界性,在此基础上,给出了H^p空间用这种面积函数的刻画,整个推理过程不用卷积与Fourier变换,因而这些结果有可能推广到没有卷积与Fourier变换的构造上去。

The Littlewood—Paley theory concerning ε—family of operators is discussed. New characterizations of Hardy spaces H^p(R^n) are given by using ε family of operators, where 0<p≤1. Since operators in ε family may not be convolutions, it iS possible to extend these results to the cases without convolution structure.