Boundedness of para-product operators on spaces of homogeneous type

We obtain the boundedness of Calderón-Zygmund singular integral operators T of non-convolution type on Hardy spaces H ^p (X) for 1/(1 + ε) < p ? 1, where X is a space of homogeneous type in the sense of Coifman and Weiss (1971), and ε is the regularity exponent of the kernel of the singular integral operator T. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature.