WEIGHTED HARDY SPACES ON SPACE OF HOMOGENEOUS TYPE WITH APPLICATIONS

Abstract

In this paper, we develop a theory of weighted Hardy spaces $H^p_\omega$ on spaces of homogeneous type and prove that certain class of singular integral operators are bounded from $H^p_\omega$ to itself and from $H^p_\omega$ to $L^p_\omega$. As an application, we give weighted endpoint estimates for Nagel-Stein's NIS operators studided in [26].