Singular integrals with flag kernels on homogeneous groups, I

Abstract

Let $\mathcal{K}$ be a flag kernel on a homogeneous nilpotent Lie group $G$. We prove that operators $T$ of the form $T(f)=f\ast \mathcal{K}$ form an algebra under composition, and that such operators are bounded on $L^p(G)$ for $1<p<\infty$.