The goal here is to study the space of functions of bounded central p-mean oscillations BCMOp and compare it to the classical John-Nirenberg space BMO. In Section 5.1 we establish some basic functional analytic results concerning BCMOp spaces on unbounded Ahlfors regular sets, including embeddings and norm characterizations. In Section 5.2 we prove the main result of this chapter which identifies the dual of the Beurling-Hardy space as the spaces of bounded central mean oscillations (see Theorem 5.1).