The decomposition of product space

In analogy with classical results [A. Bonami, T. Iwanic, P. Jones, M. Zinsmeister, On the product of functions in BMO and H1, Ann. Inst. Fourier (Grenoble) 57 (2007) 1405–1439], we prove that functions in the product of the Hardy space associated with Schrödinger operators L=−Δ+V and its dual space BMOL admit a suitable decomposition. We obtain that for and b∈BMOL, the point-wise product b⋅f as a Schwartz distribution, denoted by b×f∈S′(Rn), can be decomposed in two parts; precisely, b×f=u+v where u∈L1(Rn) while v lies in Hardy–Orlicz space associated with Schrödinger operators .