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This paper focuses on a cognitive radio network consisting of a secondary user (SU) equipped with orthogonal frequency-division multiplexing (OFDM) technology able to access N randomly fading frequency bands for transmitting delay-insensitive (e.g. data) as well as delay-sensitive (e.g. voice or video) data. Each band is licensed to a distinct delay-sensitive primary user (PU) interested in meeting a minimum rate guarantee for delay-sensitive services with a maximum allowable primary outage probability or a primary outage constraint (POC) . Typically, a PU is oblivious to the SU's existence and has its own power policy based on the channel side information (CSI) of its direct gain between the PU transmitter and the PU receiver only. Under the assumption that the SU knows PUs' power policies and CSI of the entire network, we solve the SU's ergodic capacity maximization problem subject to SU's average transmit power and outage probability constraints (SOC) and all POCs or the so-called service-outage based capacity maximization for SU with POCs. We use a rigorous probabilistic power allocation technique that allows us to derive optimal power policies applicable to both continuous and discrete fading channels. Also, a suboptimal power control policy is proposed in order to avoid the high computational complexity of the optimal policy when N is large. Numerical results are presented to illustrate the performance of the power allocation algorithms.