Multi-parameter hardy spaces via discrete Littlewood-Paley theory

In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces $ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) $ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators on $ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) $ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) and from $ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) $ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) to $ L^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) $ L^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) .