本論文的主要目的，是去討論乘積空間上的 H^p( R^n × R^m) 有界性。在這篇論文裡，應用了 Calderon 表示定理、向量值的奇異積分、Littlewood-Paley 理論、Fefferman 的矩形原子分解和 Journe 的覆蓋引理等方法去證明 T 在 H^p(R^n × R^m),max{n/(n+ε),m/(m+ε)}<p<= 1 上有界性的充分必要條件為 T*_{1}(1)=T*_{2}(1)=0，其中 ε 是關於 T 的算子核的正則指數。 The main purpose of this paper is to discuss H^p(R^n × R^m) boundedness of Calderon-Zygmund operators. We apply vector-valued singular integral, Calderon's identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journe's covering lemma to show that T is bounded on product H^p(R^n × R^m) for max{n/(n+ε),m/(m+ε)} <p<=1 if and only if T*_{1}(1)=T*_{2}(1)=0, where ε is the regularity exponent of the kernel of T.
