  Under the assumption that the underlying measure is a non-negative Radon
measure which only satisfies some growth condition and may not be doubling, we
define the product of functions in the regular $BMO$ and the atomic block
$\H^{1}$ in the sense of distribution, and show that this product may be split
into two parts, one in $L^{1}$ and the other in some Hardy-Orlicz space.
