A self-improving property of Riesz potentials in BMO

In this paper we prove that for non-negative measurable functions f, {align*} I_α f ∈ BMO(R^n) if and only if I_α f ∈ BMO^β(R^n) for β ∈ (n-α,n]. {align*} Here I_α denotes the Riesz potential of order α and BMO^β represents the space of functions of bounded β-dimensional mean oscillation.