R^n×R^m上Calderón-Zygmund算子的H^p(0<p≤1)有界性

H^p (0<p≤1) Boundedness of Calderon-Zygmund Operators in Product Spaces R^n × R^m

1 引言 在[1]中,Fefferman,R.得到了乘积空间R^m×R^m上Calderon-Zygmund算子(后文简记为CZO)理论的一个极为漂亮的结果。为叙述这一工作及本文的需要,我们先引进若干定义和记号。 称R=I×J为R^n×R^m上的二进矩形(后文简称为二进矩形)。如果I和J分别是R^n×R^m上的二进方体,记I为I的依中心扩大3倍,d_I是I的边长,x_I是其中心。

In this paper a class of Calderon-Zygmund operators in product spaces Rn× Rm is defined and it is proved that they are bounded in Hp(Rn× Rm),0<p≤1, by using the nontangential maximal function and the space's decomposition. Thus, the corresponding results in the case with one parameter are extended to the case with two parameters.