In spectrum sharing based cognitive radio networks, unlicensed users (secondary users) are allowed to communicate over the same frequency band as the licensed users (primary users) as long as the required quality-of-service (QoS) of the licensed users is guaranteed. This paper focuses on a cognitive radio network, where a secondary user (SU) sharing the same frequency band with a primary user (PU) wishes to transmit delay-insensitive as well as delay-sensitive data while the PU is interested in meeting a minimum rate guarantee for delay-sensitive services. Typically, PU's are oblivious to the SU's existence and has its own power policy based on channel side information (CSI) of its direct gain between PU transmitter and PU receiver. Under the assumption that SU knows PU's power policy and CSI of the entire network, we solve the optimal power allocation problem of maximizing SU's ergodic capacity subject to PU's outage probability constraint (POC), SU's outage probability constraint (SOC), and SU's average power constraint. We generalize earlier results which considered either ergodic capacity maximization or outage probability minimization for SU with POC, to the so-called service-outage based capacity optimization for SU with POC. We use a rigorous probabilistic power allocation technique that allows us to derive optimal power policies that are applicable to both continuous and discrete fading channels.