The authors briefly review the earlier works of multi-parameter Hardy space theory and boundedness of singular integral operators on such spaces defined on a product of Euclidean spaces, and describe some recent developments in this direction. The technique in this paper shared the deep characteristic from the previous work of Y. S. Han about Calderón’s identity. The method avoids the use of the very difficult Journe’s geometric lemma and is a unified approach to the multiparameter theory of Hardy spaces. The works include discrete multiparameter Calderón reproducing fomulas and Littlewood-Paley theory in the framework of the product of two homogeneous spaces, the product of Carnot-Carathéodory spaces, multiparameter stuctures associated with flag singular integrals and the Zygmund dilation.
For the entire collection see [Zbl 1185.35004].