Calderón-Zygmund operators on product Hardy spaces (Q961509)

The authors use the Calderón identity and Littlewood-Paley theory to show that a product Calderón-Zygmund operator introduced by Journé is bounded on product \(H^p(\mathbb{R}^n\times\mathbb{R}^m)\) for \(\max\{\frac{n}{n+\epsilon},\frac{m}{m+\epsilon}\}<p\leq 1\) if and only if \(T^*_1(1)=T_2^*(1)=0\) for some \(\epsilon>0\). Their results can be seen a further work inspired from \textit{R. Fefferman}'s work [Proc. Natl. Acad. Sci. U.S.A. 83, 840--843 (1986; Zbl 0602.42023)]. The technique in this paper shared the deep characteristic from previous work of Prof. Y. S. Han about Calderón identity.