A class of singular integrals associated with Zygmund dilations

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for these operators on $L^p,1<p<\mathrm{\infty }$, which covers those studied by Ricci–Stein \cite{RS} and Nagel–Wainger \cite{NW}