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Let $({\mathcal X},d,\mu)$ be a metric measure space of homogeneous type inthe sense of R. R. Coifman and G. Weiss and $H^1_{\rm at}({\mathcal X})$ be theatomic Hardy space. Via orthonormal bases of regular wavelets and splinefunctions recently constructed by P. Auscher and T. Hyt\"onen, together withobtaining some crucial lower bounds for regular wavelets, the authors give anunconditional basis of $H^1_{\rm at}({\mathcal X})$ and several equivalentcharacterizations of $H^1_{\rm at}({\mathcal X})$ in terms of wavelets, whichare proved useful.

Wavelet Characterizations of the Atomic Hardy Space $H^1$ on Spaces of Homogeneous Type