Discrete Calderón-type Reproducing Formula

In this paper we use the Calderón-Zygmund operator theory to provide a discrete Calderón-type reproducing formula. Since translation, dilation and, in particular, the Fourier transform are never used in the proofs, all results still hold on spaces of homogenous type introduced by Coifman and Weiss. As a consequence, we obtain a class of frames with the minimum regularity properties.