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We investigate the dynamic spectrum sharing problem among primary and secondary users in a cognitive radio network. We consider the scenario where primary users exhibit on-off behavior and secondary users are able to dynamically measure/estimate sum interference from primary users at their receiving ends. For such a scenario, we solve the problem of fair spectrum sharing among secondary users subject to their QoS constraints (in terms of minimum SINR and transmission rate) and interference constraints for primary users. Since tracking channel gains instantaneously for dynamic spectrum allocation may be very difficult in practice, we consider the case where only mean channel gains averaged over short-term fading are available. Under such scenarios, we derive outage probabilities for secondary users and interference constraint violation probabilities for primary users. Based on the analysis, we develop a complete framework to perform joint admission control and rate/power allocation for secondary users such that both QoS and interference constraints are only violated within desired limits. Throughput performance of primary and secondary networks is investigated via extensive numerical analysis considering different levels of implementation complexity due to channel estimation.