An atomic decomposition characterization of flag Hardy spaces $H^p_F({\rr}^{n}\times{\rr}^m)$ with applications

Abstract: In this paper, we give an atomic decomposition characterization of flag Hardy spaces $H^p_F({\rr}^n\times {\rr}^m)$ for $0<p\le 1$, which were introduced in \cite{hl1}. A remarkable feature of atoms of such flag Hardy spaces is that these atoms have only partial cancellation conditions. As an application, we prove a boundedness criterion for operators on flag Hardy spaces.