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 H 1 , Ann. Inst. Fourier (Grenoble) 57 (2007) 1405–1439], we prove that functions in the product of the Hardy space H L 1 associated with Schrödinger operators L = − Δ + V and its dual space BMO L admit a suitable decomposition. We obtain that for f ∈ H L 1 and b ∈ BMO L , the point-wise product b ⋅ f as a Schwartz distribution, denoted by b × f ∈ S ′ ( R n ) , can be decomposed in two parts; precisely, b × f = u + v where u ∈ L 1 ( R n ) while v lies in Hardy–Orlicz space associated with Schrödinger operators H L P ( R n , d μ ) .