The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We develop the theory of the weighted multi-parameter Hardy space H z,w p and prove the boundedness for these operators on H z,w p for certain p ≤ 1, which provide endpoint estimates for those singular integral operators studied by Ricci-Stein  and Fefferman-Pipher . We also establish the Calderón-Zygmund decomposition and interpolation theorem in this setting.
- Calderón-Zygmund decomposition
- multi-parameter singular integral operators
- weighted Hardy spaces
- Zygmund dilations