Hardy space associated with flag-type singular integrals of three parameters

Abstract

The main purpose of this thesis is to establish a Hardy space theory associated with the flag-type singular integrals on Euclidean space. This theory is a continuation of those the classical one parameter, product setting and flag setting studied by Nagel-Ricci-Stein, and includes flag-type Hardy spaces $H^p_{\mathcal{F}}$, and the boundedness of singular integrals with flag-type kernels on these spaces. The main tool of our approach is the discrete Littlewood-Paley-Stein theory associated with the flag-type structure.