We obtain the boundedness of Calderón-Zygmund singular integral operators T of non-convolution type on Hardy spaces Hp(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., Yayuan Xiao., and Obsahuje bibliografii