In spectrum sharing cognitive radio (CR) networks, secondary user (SU) is allowed to share the same spectrum band concurrently with primary user (PU), with the condition that the SU causes no harmful interference to the PU. In this letter, the ergodic and outage capacity loss constraints are proposed to protect the PU according to its service types. We investigate the performance of the SU in terms of ergodic capacity under various power allocation policies of the PU. Specifically, three PU power allocation policies are considered, namely waterfilling, truncated channel inversion with fixed rate (TIFR) and constant power allocation. We obtain the ergodic capacities of the SU under the three PU power allocation policies. The numerical results show that the PU waterfilling and TIFR power allocation policies are superior to the PU constant power allocation in terms of the capacity of the PU. In particular, it is shown that, with respect to the ergodic capacity of the SU, the PU waterfilling power allocation is superior to the PU constant power allocation, while the PU TIFR power allocation is inferior to the PU constant power allocation.