Product of functions in and ¹ in non-homogeneous spaces

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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 ¹ in the sense of distribution, and show that this product may be split into two parts, one in L¹ and the other in some Hardy-Orlicz space.