A molecular decomposition for Hᵖ(Zⁿ) and applications

In this work, for the range n-1/n < p ≤ 1, we give a molecular reconstruction theorem for Hᵖ(Zⁿ). As an application of this result and the atomic decomposition developed by S. Boza and M. Carro in [Proc. R. Soc. Edinb., 132 A (1) (2002), 25-43], we prove that the discrete Riesz potential Iα defined on Zⁿ is a bounded operator Hᵖ(Zⁿ) → Hq(Zⁿ) for n-1/n < p < n/α and 1/q = 1/p - α/n, where 0 < α < n.