Non-Isotropic Flag Singular Integrals on Multi-Parameter Hardy Spaces

Abstract

Recently, Han and Lu [HL] developed a discrete Littlewood-Paley-Stein analysis and multi-parameter Hardy space theory associated with isotropic flag singular integral operators initially studied by Muller-Ricci-Stein [MRS] and Nagel-Ricci-Stein [NRS]. The purpose of this paper is to carry out the multi-parameter Hardy space theory associated with non-isotropic flag singular integrals. The boundedness of such flag singular integral operator $T$ from $H^p_F$ to $H^p_F$ and from $H^p_F$ to $L^p$ are established in this paper. Discrete Calderón's identity and Min-Max principle derived here are the main tools used to establish the non-isotropic multi-parameter Hardy space theory.