In this paper, we study the ergodic capacity ofCognitive Radio (CR) spectrum sharing systems at low power regime. We focus on Nakagami fading channels. We formally define the low power regime and present closed form expressions of the capacity in the low power regime under various types of interference and/or power constraints, depending on the available channel state information (CSI) of the cross link (CL) between the secondary user transmitter and the primary user receiver. We explicitly characterize two regimes where either the interference constraint or the power constraint dictates the optimal power profile. Our framework also highlights the effects of different fading parameters on the secondary link ergodic capacity. Interestingly, we show that the low power regime analysis provides a specific insight on the capacity behavior of CR that has not been reported by previous studies.